From Starfarer

United Federation (of Planets) Marshal Service

The United Federation Marshals Service is responsible for apprehending wanted fugitives, providing protection for the Federation judiciary, transporting Federation prisoners, protecting endangered Federation (and allied) witnesses, managing assets seized from criminal enterprises and liaising with friendly agencies of external powers on joint law enforcement issues.

The United Federation Marshals Service also executes all lawful writs, processes, warrants and orders issued under the authority of the Federation Courts, the Federation Council and the Federation President and may command all necessary assistance to execute its duties. The Marshals, unless they have no other choice, or are so requested by JAG or NCIS, do not pursue marine or Starfleet fugitives.

Federation Marshals also have the common law based power to enlist any willing Federation citizens as special deputies. This stems from the old traditions of the United States Marshal Service, though under the Federation Comitatus Act (passed 2289, amended 2364) they cannot enlist serving marines for law enforcement duties.