It depends but if you are required to file a federal income tax return then you will need to file a GA nonresident state income tax return regarding this GA-sourced interest income.
Since the property for which you are receiving this interest income is located in GA, this interest income is considered GA-sourced income.
According to the GA Department of Revenue, nonresidents who receive income from Georgia sources and are required to file a Federal income tax return, are required to file a Georgia income tax return.
Usually, you will get a state tax credit in your home state for any nonresident state taxes paid to another state on out-of-state sourced income. However, since FL has no individual state income taxes, no GA state tax credit will be available.