This year you should be okay filing only a Georgia return. I do want to make you aware of a provision in the tax law that became available this year, which you can see at this link: Veterans Benefits and Transitions Act of 2018 Through this Act, a military couple may now unite their states of residence for tax filing purposes.
Due to this act, you as a Military spouse may claim Ohio as your state of residence as well. (You are not required to, but you may). Doing so this year might not make much sense: you would have to file a Georgia return to get a refund of Georgia tax, but you would pay tax to Ohio. You may also decide that for this year (2019), you wish for the same treatment (just to keep your tax return as simple as possible).
However, for 2020, you may decide to elect Ohio as your state of residence. This would certainly be true if you are PCS'd to another state because it would be much more complicated for you to file if you maintain Georgia (you would still file a Georgia return, but also a return for that state also, since your income is not covered by the MSRRA unless you and your husband share the same home of record).
But it could also be the case even if you continue to stay in Georgia, if Ohio tax is lower than Georgia tax, for instance. That decision in the end is yours to make, but you do have that option available to you.
However, this year you should be able to file as you have in the past: you file your income for Georgia, and your husband does not have to file a return.
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