This permit is issued by the Florida Department of State, not by local law enforcement agencies. You can either call or write to them and make a specific request for a Concealed Weapon Permit. Information is available online at the Department of State’s web site, or you can contact them by phone or mail:

Florida Department of State
Division of Licensing
Post Office Box 6687
Tallahassee, FL 32314-6687
(850) 488-5381

However, you may visit the FBPD records department and recieve a packet containing all you need to know about obtaining a Concealed Weapons Permit.