There is no state income tax in Florida, so you don't need to worry about that.
I'm not sure if you mean you live in an apartment that you are renting, or if you are renting it to someone else. If you are renting the apartment to someone else, see the following:
There is a tangible property tax return however, that you need to file if you have furniture and fixtures for the rental property. Property that totals less than $25,000 does not get taxed, but you need to file the tangible property tax return in the first year you are renting to qualify for the exemption. After the first year, you don't need to file the return again unless your property is over $25,000.
Here's a link to the Florida Department of Revenue:
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