You file a non-resident NJ return in addition to your home state NY return. You'll be able to take a credit on your home state NY return for taxes paid to the non-resident state (NJ).
In TurboTax, complete the non-resident return before you do the home state return, so that the credit flows properly.
This FAQ explains the process in TurboTax: https://ttlc.intuit.com/questions/1901271-how-do-i-file-a-nonresident-state-return
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
