If you live in New Jersey because your service member spouse is stationed here but you are not a New Jersey resident, you do not pay New Jersey income tax on wages you earn in the state. For state tax purposes you can choose your own home state, the state where your spouse is stationed, or your spouse’s state of legal residence. You can make that choice even if you never lived in that state, and even if you did not live with your spouse during the tax year.
There is nothing to apply for in advance. Do not report New Jersey wages as New Jersey taxable income, and tell your employer which state of residence you have chosen so withholding is set up correctly. If New Jersey tax was already withheld, file a New Jersey nonresident return to claim the refund.
Your marriage certificate, your spouse’s military orders assigning them to New Jersey, and proof of the state of residence you are claiming.