Georgia state tax refunds can take a long time to process. According to the Georgia DOR website, possibly even more than 90 business days.
However, we can tell you some things to check.
If you efiled the state return, use the tool below to be sure the state return was successfully efiled and accepted:
https://shop.turbotax.intuit.com/efile/efile_status_lookup.jsp
If that confirms it was accepted, or if you mailed the state return, then here's how to check the status of a state refund.
FAQ: How do I track my state refund?
https://ttlc.intuit.com/replies/3300211