A police department is where all the recidivists get locked up and do their time. There are various local police departments across the map where cops usually start their duty at. Suspects can pay outstanding tickets and felonies can turn themselves in by surrendering at any PD should they feel like it from the checkpoint.
Civilians with clean record can enlist as a police officer at any closest PD. Oh and be careful while engaging in shady activities like attempting bribe around these places as there's a good chance that the bribes could be refused, which will result in your money to be confiscated - this could increase heat that could only put you in even more trouble.
You can find police departments across the map with the following icon: 
Police mechanic checkpoints are shown with the icon: 
Police Offices
Every real-life Saturday, Workers of the Week are chosen based on their total earnings during the week. Among them, there are 5 Comissioners (police officers) assigned basing on money earned on police activities. They are set on different police stations around the map, these being Mission Row, Davis, La Mesa, Sandy Shores and Paleto Bay.
Comissioners can use their offices to refill donuts for free and collect their daily payout which is based on the 'prestige' of the office and criminals arrested in their respective jurisdiction. Additionally, they can use their respective police garage without spending police credits. They also have access to exclusive police vehicles labeled as "Comissioner Vehicles" on their respective police garage for free.
Comissioners can be recognized by an unique star next to the nickname tag (Blue).