Can you elaborate on your situation? Did you move to NY from NJ? Were you working in NJ?
If you moved during the year, you would complete a part-year resident return for each state. The income will be taxed by the state in which it was earned, but it will also be taxed by your resident state. If you worked in NJ but moved to NY, you will still have a tax liability to NJ, but any overpayment because of a change in residence will be refunded when you complete a part-year resident return.
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