The Patrol is the military arm of the Federation. They have access to the fastest and most heavily armed ships in the Federation. Even worse for law breakers, their ships have military vehicles: flamers (flamethrower tanks) and mauls (artillery capable of downing a starship.
In spite of bearing weapons of mass destruction the Patrol does not use lethal force until more humane means fails. They typically carry high powered but non-lethal stun rifles and demand surrender of suspects or outlaws. In the event of a gun battle they can and will bring every means they have to win including heavy weapons.
A lot of the Patrol's duties seem to involve Trade. Merchant ships must file a flight plan and a passenger list for each voyage. The Patrol runs background checks on all passengers before a flight is okayed functioning like an internal security department. They also man a wide network of emergency resupply stations across the Federation to aid ships in need. There most unenviable job is locating plague ships and disposing of the same by hurling them into suns.
The Patrol can also Post especially violent or dangerous criminals. Being Patrol Posted is equivalent to being an outlaw. Federation citizens can shoot you on sight with no legal repercussions. Likewise once a ship is determined to be a plague carrier Patrol forces can open fire on that ship with no warning and show no mercy.
In spite of its impressive weaponry the Patrol doesn't always keep the peace. Federation worlds will have armed altercations and even war with the Patrol doing little besides enforcing a blockade to keep these conflicts from spreading. The fact is the galaxy is a big place and they can't be everywhere at once. Stopping two high population, high technology worlds from fighting would strip entire sectors of their defenses and leave them open to pirates. The greater good forces the Patrol admiralty to take a passive seat at times.
Trade and Patrol often work together to keep the peace, with Trade forging bonds of trade to make conflict unprofitable. The Patrol regards Trade as an equal partner in keep ing the peace. It certainly regards Trade's activities and vital to the continued existence of the Federation and devotes a lot of effort to protecting merchant shipping (mostly that of the big companies though). Free traders can expect any reasonable aid and to be treated with respect though they might be watched closely.
A disturbing trend lately is the attempts of the sector control offices to field their own forces and keep Central Control out of the loop or even deny funding and materials to local Patrol ships. The Patrol Admiralty is pursuing these isolationists and attempting to shut down their activities. At this time most sector chiefs strongly support the Patrol.