As the spouse of an active duty servicemember, you are permitted to use his State of Legal Residence (SLR) as your own home state for state tax filing purposes. You may also use your own home state if you prefer. It's your choice.
So if your servicemember's spouse's SLR is GA, you may choose to file only in GA.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.