If you are the spouse of a service member stationed in Georgia and neither of you is a Georgia resident, you do not owe Georgia income tax on what you earn here.
Claim the exemption when you file, and give your employer a Georgia withholding certificate so that Georgia tax is not withheld from your pay. The individual income tax booklet explains the filing steps.
Proof that you and the service member share a legal residence outside Georgia, the service member’s orders assigning them to Georgia, and your marriage certificate.