NTC Nuveen Connecticut Quality Municipal Income Fund

SCHEDULE 13D

SCHEDULE 13D

This Statement on Schedule 13D (this “ Statement ”) relates to the purchase of variable rate munifund term preferred shares (“ VMTP Shares ”) of Nuveen Connecticut Premium Income Municipal Fund (the “ Issuer ” or the “ Company ”). This Statement is being filed by the Reporting Persons (as defined below) as a result of the purchase of VMTP Shares by Capital Strategies (as defined below). The Issuer’s principal executive offices are located at 333 West Wacker Drive, Chicago, IL 60606.

This Statement is being filed on behalf of each of the following persons (collectively, the “ Reporting Persons ”):

i. Wells Fargo & Company (“ Wells Fargo ”)

ii. Wells Fargo Municipal Capital Strategies, LLC (“ Capital Strategies ”)

This Statement relates to the VMTP Shares that were purchased for the account of Capital Strategies.

The address of the principal business office of Wells Fargo is:

420 Montgomery Street

San Francisco, CA 94104

The address of the principal business office of Capital Strategies is:

375 Park Avenue

New York, NY 10152

Wells Fargo and its subsidiaries provide banking, insurance, trust and investments, mortgage banking, investment banking, retail banking, brokerage services, and consumer and commercial finance through more than 9,000 stores, 12,000 ATMs, the internet and distribution channels to individuals, businesses and institutions across North America and internationally. The principal business of Capital Strategies is to make investments and provide loans to clients.

Information concerning each executive officer, director and controlling person (the “ Listed Persons ”) of the Reporting Persons is listed on Schedule I attached hereto, and is incorporated by reference herein. To the knowledge of the Reporting Persons, all of the Listed Persons are citizens of the United States, other than as otherwise specified on Schedule I hereto.

Other than as set forth on Schedule II, during the last five years, none of the Reporting Persons, and to the best knowledge of the Reporting Persons, none of the Listed Persons, have been convicted in a criminal proceeding (excluding traffic violations or similar misdemeanors) or was a party to a civil proceeding of a judicial or administrative body of competent jurisdiction as a result of which such person was or is subject to a judgment, decree or final order enjoining future violations of, or prohibiting or mandating activities subject to, federal or state securities laws, or finding any violation with respect to such laws.

The aggregate amount of funds used by the Reporting Persons to purchase the securities reported herein was approximately $106,000,000. The source of funds was the working capital of the Reporting Persons.

The Reporting Persons declare that neither the filing of this Statement nor anything herein shall be construed as an admission that such person is, for the purposes of Section 13(d) of the Exchange Act or any other purpose, (i) acting (or has agreed or is agreeing to act together with any other person) as a partnership, limited partnership, syndicate, or other group for the purpose of acquiring, holding or disposing of securities of the Company or otherwise with respect to the Company or any securities of the Company or (ii) a member of any group with respect to the Company or any securities of the Company.

Capital Strategies has purchased the VMTP Shares for investment purposes. Capital Strategies acquired the VMTP Shares directly from the Company pursuant to a Purchase Agreement, dated February 21, 2014, between the Company and Capital Strategies (the “ Purchase Agreement ”) on their initial issuance for a purchase price of $106,000,000.

The Reporting Persons have not acquired the subject securities with any purpose, or with the effect of, changing or influencing control of the issuer, or in connection with or as a participant in any transaction having that purpose or effect.

(a)—(b) The responses of the Reporting Persons to Rows (7) through (11) of the cover pages of this Statement are incorporated herein by reference.

(c) The responses of the Reporting Persons in Item 3 and Item 4 are incorporated herein by reference.

(d) No other person is known by the Reporting Persons to have the right to receive or the power to direct the receipt of dividends from, or the proceeds from the sale of, VMTP Shares that may be deemed to be beneficially owned by the Reporting Persons.

(e) Not applicable.

The responses of the Reporting Persons to Item 4 are incorporated herein by reference. With respect to the VMTP Shares owned by Capital Strategies, on February 21, 2014, Capital Strategies assigned certain preferred class voting rights on the VMTP Shares to a voting trust (the “Voting Trust”) created pursuant to the Voting Trust Agreement, dated February 21, 2014 among Capital Strategies, Lord Securities Corporation, as voting trustee (the “Voting Trustee”) and Institutional Shareholder Services Inc. (the “Voting Consultant”). Voting and consent rights on the VMTP Shares not assigned to the Voting Trust have been retained by Capital Strategies. The Voting Trust provides that with respect to voting or consent matters relating to the voting rights assigned to the Voting Trust, the Voting Consultant analyzes such voting or consent matters and makes a recommendation to the Voting Trustee on voting or consenting. The Voting Trustee is obligated to follow any such recommendations of the Voting Consultant when providing a vote or consent. Capital Strategies has the right to cause the Company to register the VMTP Shares pursuant to a Registration Rights Agreement, dated February 21, 2014 between the Company and Capital Strategies.

SIGNATURES

After reasonable inquiry and to the best of my knowledge and belief, I certify that the information set forth in this statement is true, complete and correct.

Date: February 28, 2014

LIST OF EXHIBITS

SCHEDULE I

EXECUTIVE OFFICERS AND DIRECTORS OF

REPORTING PERSONS

The following sets forth the name and present principal occupation of each executive officer and director of Wells Fargo & Company. The business address of each of the executive officers and directors of Wells Fargo & Company is 420 Montgomery Street, San Francisco, CA 94104.

The following sets forth the name and present principal occupation of each executive officer and director of Wells Fargo Municipal Capital Strategies, LLC.

Schedule II

AUCTION RATE SECURITIES (LEGACY WACHOVIA) Beginning in August 2008, Wachovia Securities, LLC, n/k/a Wells Fargo Advisors LLC (Wachovia Securities) and Wachovia Capital Markets, LLC, n/k/a Wells Fargo Securities LLC (collectively with Wachovia Securities, the Wachovia Securities Affiliates) entered into settlements agreements with state regulatory agencies, including the Secretary of State for the State of Missouri (as the lead state in the North American Securities Administrators Association task force investigating the marketing and sale of auction rate securities), relating to investigations of sales practice and other issues related to the sales of auction rate securities (ARS). Wachovia Securities also announced a settlement in principle with the Securities and Exchange Commission (SEC) of its similar investigation. Without admitting or denying liability, the agreements required that the Wachovia Securities Affiliates purchase certain ARS sold to customers in accounts at the Wachovia Securities Affiliates, reimburse investors who sold ARS purchased at the Wachovia Securities Affiliates for less than par, provide liquidity loans to customers at no net interest until the ARS are repurchased, offer to participate in special arbitration procedures with customers who claim consequential damages from the lack of liquidity in ARS and refund refinancing fees to certain municipal issuers who issued ARS and later refinanced those securities through the Wachovia Securities Affiliates. Without admitting or denying liability, the Wachovia Securities Affiliates also agreed to pay a total fine of $50 million to the state regulatory agencies and agreed to the entry of consent orders and Wachovia Securities agreed to entry of an injunction by the SEC.

AUCTION RATE SECURITIES (LEGACY WELLS FARGO) Beginning in November 2009, three broker-dealer subsidiaries (the Broker-Dealer Subsidiaries), Wells Fargo Investments, LLC, Wells Fargo Securities, LLC (as successor to Wells Fargo Brokerage Services, LLC), and Wells Fargo Institutional Securities, LLC, of Wells Fargo & Company (“Wells Fargo”) entered into settlement agreements with state securities regulators regarding the Broker-Dealers Subsidiaries’ participation in the auction rate securities (ARS) market. Under the agreements, the Broker-Dealer Subsidiaries agreed to purchase Auction Rate Securities (ARS) from eligible investors that bought ARS through the Broker-Dealer Subsidiaries prior to February 13, 2008 and to cease and desist from certain activities. Without admitting or denying liability, Wells Fargo Investments, LLC, agreed to pay $1.9 million in fines and penalties and the Broker-Dealer Subsidiaries agreed to reimburse investigative expenses.

ULTRASHORT OPPORTUNITIES FUND INVESTIGATION On June 8, 2009, the SEC and the Massachusetts Securities Division entered administrative orders against two subsidiaries of Wells Fargo & Company, Evergreen Investment Management Company LLC and Evergreen Investment Services Inc., with respect to certain alleged conduct involving the Evergreen Ultrashort Opportunities Fund (the Fund). The allegations included the misvaluation of certain holdings in the Fund thereby affecting the Fund’s net asset value (NAV), and improper disclosure of information concerning the Fund. Without admitting or denying the allegations, the firms agreed to a censure and cease and desist order from both agencies, a payment of $33 million for investors, disgorgement of $2.86 million plus prejudgment interest to the SEC, a $4 million penalty to the SEC, and a $1 million penalty to the Massachusetts Securities Division.

MUNICIPAL DERIVATIVES BID PRACTICES INVESTIGATION The Department of Justice (DOJ) and the SEC, beginning in November 2006, requested information from a number of financial institutions, including Wachovia Bank, N.A.’s (n/k/a Wells Fargo Bank, NA) municipal derivatives group, with regard to competitive bid practices in the municipal derivative markets. Other state and federal agencies subsequently also began investigations of the same practices. On December 8, 2011, a global resolution of the Wachovia Bank investigations was announced by DOJ, the Internal Revenue Service, the SEC, the Office of the Comptroller of the Currency and a group of State Attorneys General. The investigations were settled with Wachovia Bank agreeing to pay a total of approximately $148 million in penalties and remediation to the various agencies.

ASSET-BACKED COMMERCIAL PAPER INVESTIGATION On August 14, 2012, the SEC entered a settled administrative order against Wells Fargo Brokerage Services LLC (n/k/a Wells Fargo Securities, LLC) and a former sales representative concerning alleged sales practice and suitability issues related to certain 2007 sales of three asset-backed commercial paper products to institutional and municipal purchasers. Without admitting or denying the allegations, the firm agreed to a censure, a cease-and-desist order, disgorgement of $65,000 plus prejudgment interest, and a civil penalty of $6.5 million.

ABS CDO INVESTIGATION In April of 2011, Wells Fargo Securities, LLC (f/k/a Wachovia Capital Markets, LLC) entered into a settlement with the SEC in which the firm paid $11.2 million in disgorgement and penalties and agreed to cease and desist from violating Sections 17(a)(2) and (3) of the Securities Act, in order to resolve issues arising from an investigation into Wachovia Capital Markets, LLC’s ABS CDO underwriting, marketing and pricing practices.