You have a situation of dual residency. You are domiciliary residents of NY and statutory residents of CT. Therefore you must file as a resident in each of the two states.
You may take a credit on your CT return for the taxes paid to NY, so in effect you won't be double-taxed. See this reference for details:
https://portal.ct.gov/DRS/Publications/Special-Notices/1992/SN-92-2
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
