Here are New York's filing requirements for non-residents: https://www.tax.ny.gov/pit/file/nonresidents.htm
Remember that ALL your income is taxable by CT, regardless of where you earned it. The question is whether or not you also have to file a non-resident return in NY.
If you have to file in NY, you'll be able to take a credit on your CT return for taxes paid to NY - so you won't be double-taxed. (In that situation, be sure in TurboTax that you complete your non-resident tax return before you do your home state return.)
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
