You'll have to submit the requested forms. If your wife never worked a day in New York, she'll owe no NY income tax and you should receive a refund of all the withheld NY tax.
If she worked both remotely and in person in New York, NY will want to know if the remote portion of her work was done by her own choice for convenience' sake, or because she was required to work remotely by her employer. If she worked remotely for her own convenience, NY may tax that remote income.
If you do have to pay NY income tax, you'll be able to claim a "other state credit" on your CT tax return for the taxes paid to NY, so as to offset any double taxation.
If she still has the same employment situation, she should complete NY Form IT-2104.1 and submit it to her New York employer. Here's a link to the form:
https://www.tax.ny.gov/pdf/current_forms/it/it2104_1_fill_in.pdf
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
