It depends - You can file jointly for federal and file married filing separately for state tax purposes even if you live in the same state (both live in NJ and work in NY). However, you cannot file your resident state return (NJ) jointly but file your nonresident state return (NY) as married filing separately. You either have to file both states jointly or both states separately.
Also, you may want to run 2 sets of state returns to determine if filing separately for state tax purposes will provided you with a lower state income tax liability then just filing your state jointly.
If you decide to file your state return's separately, please review the following information:
https://ttlc.intuit.com/replies/3301995