You will need to fill out the NY part-year first. You will also need to know how much you made during the time that you lived in NJ. If you told your payroll department about the move when it happened you should have a NJ line in the state section of your W-2. At that point (unless you are a city employee) the NYC tax should have stopped. You would then get a credit on your NJ return for taxes paid to NY for income taxed by both states.
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