I am not a tax professional, so you will need to verify this answer with a professional. But from what I have learned as a taxpayer, it sounds like you will need to fill out a federal return, a state return for NY, and a state return for NJ. On the NJ return, you will fill in that you had no NJ income, but you will also fill in on the NJ return the amount of state tax that NJ withheld. Therefore NJ will owe you a state tax refund via your NJ tax return.
