No. Florida does not have an individual income tax so there is nothing you need to file with the state.
However, if you use tangible personal property in connection with your rental (e.g., furnishings), then you may have to establish an account with your county's property appraiser and then file a Form DR-405 to report that personal property.
You can visit your county property appraiser's web site for further information (see link below).
http://floridarevenue.com/property/Pages/LocalOfficials.aspx