Live and work remotely in NYC for a company based in CT

You need to file a New York (NY) state resident tax return and a Connecticut (CT) non-resident tax return.  When you enter your W-2 you will fill out the state information for the first state listed on your Form W-2.  You will then add a state and fill out the information for the second state.   As a New York resident, they will tax your income regardless of where it is earned.  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.  New York will give you a credit for taxes paid to other states (In your case Connecticut ) so the income is not double-taxed.  The credit amount may be the same or less than the CT tax you pay, but it will not be more.