Connecticut has a Convenience of the Employer rule that applies to states that have a similar rule (which includes New York). Connecticut requires New York residents who work remotely for a Connecticut employer to file a nonresident tax return reporting all income. You will then be able to claim a credit on your New York state return for the taxes paid to Connecticut so the income is not double-taxed.
[Edited 04/17/23| 2:15pm PST]
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