this is a question that is determined by what state you're in.  In pennsylvania, and probably most states, municipal cops can only make a bust in their muncipality. State cops, obviously, can bust someone anywhere in the state.  Never fear, though, most local cops have worked out how to hold a suspect until someone from the "correct" department arrives on the scene to actually make the arrest.  Or, if they see a speeding car in another jurisdiction, call it in to the right folks.

It depends on some variables.  Sherrifs and deputies usually can make arrests anywhere within their county, while in some places Local cops are deputized by the sherrif department to make arrests outside city limits.  Other places, this isn't so.

http://courtofappeals.mijud.net/Digest/newHTML/11861511.htm

This isn't on florida but it talks a lot about citizen arrest.

I know in SC if a police officer witnesses a crime, he can hold the person and call the local police. I still wave on the Goose Creek police when I am speeding past them in N.Charleston. I never drive fast or dangerous enough for them to pull me over but I have fun doing it.

found this link too..good question...I want to know too as I am going to tour in florida and other cities too

http://www.postgazette.com/nation/20020809ring6.asp