Timo said:
The thing is, onscreen we have never seen any sort of a local police force on any known UFP member world. If there has been local police, it has been an organization somewhat at odds with Starfleet and the Federation, such as on that mining planet in DS9 "Progidal Daughter".
On Earth, Starfleet seems to perform the FBI role: hunting for spies and Maquis. Starfleet also seems to enjoy complete jurisdiction over its own personnel, regardless of the nature of the crimes they commit: it seems to be Starfleet that chases Harry Kim or Leonard McCoy in San Francisco, and takes custody after an arrest is made, operating a gaol of its own somewhere in the city.
The existence of planet-specific intelligence services is confirmed, though: Vulcan has one in "Unification" at least. And then there's this Federation Security, whatever that is, that sends its agent to arrest McCoy and deliver him to Starfleet hands.
I'm not sure it would be that bad an idea to have Starfleet handle everything from municipal sanitary services to counterespionage. A "separate" police organization wouldn't really be qualitatively different: its leaders, too, would ultimately be responsible to some Minister in the cabinet of Federation Prime Minister (as novels suggest) or President (since onscreen we don't hear of a Prime Minister, and the President is shown making major non-ceremonial decisions, suggesting a system where either the President is the Prime Minister or else he or she has political powers over the Prime Minister).
Does it really matter whether the head of police is the Minister of Interior or the Minister of Defense? Totalitarian regimes do just fine with delegating the police work to Interior, while free democracies could plausibly be construed with militia-type law enforcement agencies.
Given the blatant lack of references to civilian police, I'd tend to think that Starfleet indeed is the Federation police, and possbily also that there is no local police as such. Remember that this is the brave new world where criminal tendencies are screened against at youth, and criminals are always considered mentally ill and cured of their vices after arrest. The need for policing would be very different from the needs today: if there is violent crime, it's probably in the form of massive riots where "justified" passions surface, not in the form of private acts of "criminal" aggression. And if those riots erupt, then it obviously is time to call in Starfleet...
Timo Saloniemi