In order to get a refund of the incorrectly withheld Arkansas taxes, she must file a non-resident Arkansas tax return, showing zero Arkansas income.
She must file the AR tax return on paper, and she must attach Arkansas Form AR-MS to it. Here's a link to that form: https://www.dfa.arkansas.gov/images/uploads/incomeTaxOffice/AR-MS.pdf
You and your wife can file jointly in your home state of Georgia.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
