FE962/FE962: Handbook of Florida Fence and Property Law: Trees and Landowner Responsibility pretty much covers it.
In general, you may cut the limbs and roots at or inside your property line at your expense. I would have a survey done before doing that if you are going to cut it close.
A surprising result was a case that prevailed when the owner cut down a tree and the owner of the adjoining property was compensated for the impact, loss of shade!
If you do it, it may look unsightly.
(This is not legal advice. IANAL)