Income you earn in Rhode Island is exempt from Rhode Island income tax if you are the nonresident spouse of a nonresident service member stationed in the state. You qualify only if you are in Rhode Island because your spouse is stationed there and the two of you have the same state of residence.
There is nothing to apply for. Leave the exempt Rhode Island wages off your Rhode Island return, and ask your employer to stop withholding Rhode Island tax.
Your marriage certificate, your spouse’s orders assigning them to Rhode Island, and proof that you and your spouse share the same state of residence.
