If you are a nonresident service member stationed in Arkansas and you and your spouse share the same home state outside Arkansas, neither of you owes Arkansas income tax. You still owe tax in your home state if that state requires it.
There is nothing to apply for with Arkansas. File in your home state instead, and give your employer your home state of residence so Arkansas tax is not withheld. If Arkansas tax was withheld, file an Arkansas nonresident return to claim the refund.
Your military orders assigning you to Arkansas and proof that you and your spouse share the same state of legal residence.
