No, you are not required to pay Georgia taxes if your home of record is Florida (and you don't have income such as rental income from a property in Georgia). Have you ever declared a home of record other than Florida?
You do have the option of filing a joint return as if you were both residents of Georgia. If you choose to do this, it doesn't matter where your home of record is.
Per Georgia instructions, "if one spouse is a resident and the other is a nonresident without any Georgia-source income, your Georgia return may be filed jointly or separately with each spouse claiming the appropriate exemptions and deductions. "
If you don't want to file a joint return with Georgia:
If your name is listed first in Turbo Tax, then it is recommended that you create a separate Turbo Tax username to file your spouse's GA separate return. To do so, you would input only his/ her income in the federal areas a "Married Filing Separately". This creates a "mock" federal return which will flow into the Georgia return. Obviously, don't file the federal one.
If your spouse's name is listed first, she should have the option of whether or not to file jointly or separately in the State taxes tab. In some cases, you can still be better off filing a joint return.
Questions? Please ask.