You can't e-file a state return in Turbotax unless you e-file a federal return at the same time. If you already filed someplace else, you can't use Turbotax to e-file a state return.
You could purchase Turbotax (either online or to install on your own computer), prepare a new federal return, then prepare a state return, and print and mail the state return. However, if you don't qualify for free filing, you would have to pay for both the federal and state return even though you don't need the federal return. I think the cheapest current price is something like $29+$39 online, or $45 for Turbotax Deluxe Federal+State through Amazon.
You might also be able to e-file for free online directly on the GA income tax web site, if you have a printout of your federal return and can follow the instructions.
