Since you live in Connecticut you must file a CT resident tax return, no matter where you earn your income. As a CT resident, all your income is subject to CT tax, no matter where the income is from. You must also file a NY nonresident tax return and pay NY tax on the income that you earned in NY. Income that you earn for working in NY is subject to NY tax, even though you don't live in NY. You will get a credit on your CT tax return for part or all of the tax that you pay to NY.
At the beginning of the TurboTax interview, when you enter your personal information, it asks you what state you live in. You will indicate CT. Then it asks whether you had income from any other state. Answer Yes and select NY as the other state. When you get to the State section, after finishing your federal tax return, it will prompt you to prepare tax returns for both states. Prepare your NY nonresident tax return first, then your CT resident tax return.
