If CT is your domicile state, then you must file a full-year resident CT tax return, and ALL your income is taxable by CT, regardless of its source, and regardless of whether or not you have a CT drivers license.
If you have no NY-source income, then you need not file a non-resident NY tax return. Caution: if you work in New York even for a single day, then you may have NY-source income. Post back for details if this is your situation.
https://www.tax.ny.gov/pit/file/nonresident-faqs.htm
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
