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The GA IT-511 income tax booklet states:

 

"A married part-year resident or nonresident with income earned in Georgia whose spouse is a nonresident with no Georgia source income may file either a separate return claiming only their own personal exemption and dependent exemptions and deductions or a joint return claiming total allowable deductions."

 

While you are free to work GA both ways, because GA has a progressive tax system, the couple of thousand would be taxed at a marginal rate of 3% for MFS and, most likely, 5.75% for MFJ.