Q: "Is it the case I can just apply my CT state tax as a credit against my NY state tax?"
A: Yes. You may claim a credit on your NY state tax return for taxes paid to CT on the income that is taxed by both.
With regard to withholding, assuming your Connecticut employer is not incorporated or licensed under New York state law and does not maintain an office in New York, as an out-of-state employer it is not required to withhold New York state income taxes for its New York resident employees.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
