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 temp cop 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: and PD mechanic checkpoints are shown wih the icon: