You file in both states. New York taxes all of your income because you live there. Connecticut will tax your income on work you performed there. To reduce double-taxation, New York will give you a credit for the tax you pay to Connecticut for the income you earned in Connecticut.
To make sure that this credit transfers over to the New York return, prepare the Connecticut nonresident return first, and then the New York resident return. (Since you worked outside of New York City, you will not have to pay NYC tax on that income, but you will pay NY state tax above what Connecticut taxes the income).
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