The Stilwater Police Department Headquarters is located in the Harrowgate neighborhood of the Saint's Row District.
Shaundi and The Protagonist enter the headquarters in order to tap into the traffic surveillance system to find The General. The title of the mission is the only time it is ever referred to as "Precinct 31", and that name does not appear in dialogue during the mission or at any other point in the game.
There are 3 phone tap recordings in the Stilwater Detective Bureau on the third floor. After listening to them, a file on Julius becomes available in Chief Bradshaw's office, which contains Dex's phone number. Calling Dex unlocks the bonus mission.
The Police Headquarters is build on the site of the docks from the mission Reclamation, in which Troy was a Homie and shot at cops.
Male officers may enter the female locker room, and vice-versa
There is a darkened sign in the third floor that reads Dead end, following the sign leads to a dead end.
In the office before Troy's, as well as in other places in the Police Headquarters, is a framed "Certificate of Achievement" which reads: "You can't imagine how proud we are of you. Please let us fuck your daughter. Pretty please with a cherry on top. Thanks, Will Trustworthy".