The 1099 is a large family of forms, used to report many different kinds of income. The answer to your question will depend on specific factors not mentioned in your question.
If you received a Form 1099-MISC reporting rents earned on a property in Georgia or non-employee compensation earned by working in Georgia, the State of Georgia is going to expect you to file a nonresident tax return and pay taxes on your Georgia-sourced income. Of course, this is also subject to you having enough income to require the filing of a Georgia tax return.
On the other hand, if you have a Form 1099-R reporting retirement income paid to you in Florida from a Georgia-based bank or insurance company, that would not require the filing of a Georgia tax return.
