"do you have to purchase and file Florida State forms?"
Florida does not levy a state individual income tax. You do not need to file an income tax return with the state.
The Florida return in TurboTax is to report tangible personal property that is used in a Florida-located business or rental property and is filed with the county property appraiser by April 1st.
If you have a rental property in Florida and use tangible personal property in connection with that property (e.g., furnishings), then you may have to establish an account with the county property appraiser and file a Form DR-405 to report that property. For further information, select your county at the link below.