" Cocoon’s central government, the Sanctum, holds supreme executive, legislative, and judicial power. It also maintains directive authority over the military. " - Datalog: Cocoon Society.
Under the leadership of the Primarch Galenth Dysley and the guidance of the fal'Cie Eden, the Sanctum rules over Cocoon and is responsible for law enforcement and every political decision that shapes Cocoon's future. Despite the fact that the fal'Cie control many of the things responsible for sustaining Cocoon, they take only a passive interest in governance and leave the bulk of it to the Sanctum.
There are two arms of law enforcement, PSICOM and the Guardian Corps, with each responsible for different things. The Sanctum also uses them to enact the Purge, when it is feared a citizen has come into contact with anything from Pulse, and to generally keep the peace in Cocoon.