Under Special Rules for Married Individuals on page 1 of this CT tax reference, scroll down to the paragraph on non-resident aliens. You'll find your filing options there.
https://portal.ct.gov/-/media/DRS/Forms/2022/Income/2022-CT-1040NRPY-Instructions_1222.pdf
And this reference gives your filing status options for your New York tax return:
https://www.tax.ny.gov/pit/file/filing_status.htm
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
