See this TurboTax help article regarding New Jersey residency and working in New York. You will need to file a Resident NJ return and a Nonresident NY return.
Depending on your individual situation, it may be better to file jointly for the Federal return and separate State returns. Some tax benefits aren't available for Separate filing status.
You can use TurboTax Online to test different scenarios before deciding to file jointly or separately. Click here for more information from TurboTax on how to decide which filing status to choose.
See here for a discussion and steps to file a joint Federal return and separate State returns.
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