Florida does not impose an individual income tax so you do not need to file any kind of income tax return with the state.
However, counties in Florida are authorized to impose a tangible personal property tax on assets used in businesses and rental real estate located in Florida (essentially, this tax is the same as your real estate tax only imposed on certain personal property).
You can read more about the tangible personal property tax at the links below. The second link is a list of web sites of county property appraisers which will provide you with specific information for the county in which your rental is located.
http://dor.myflorida.com/dor/property/tpp/
http://dor.myflorida.com/dor/property/appraisers.html
