Most towns will have a police presence from the start of the campaign.
They are generally lightly armed, and limited in numbers.
They will take actions against you (and other civilians) if provoked.

Police Station

Towns with a police presence will also have a local police station.
This will generally be lightly manned, and contain crates with basic police equipment and some building supplies.

Police Reinforcements

When taking casualties the police will call in reinforcements.
These reinforcements are in-exaustable.
The only way to stop them is to stop killing the police, kill them all quickly enough that they cannot call for reinforcements, or to liberate the town.

Police Dialogues

You can talk to policemen. They are willing to suppress active civilians, which you can exploit.

Ask About A Police Station

Policeman will tell you where the nearest police station is.

Report Rebel Activity

You can lie (or maybe not lie?) about some rebel activity to the policeman. There are two options. You can tell them to follow you (so that you can point at what you have found). Or you can point in general direction, and the police will run there to investigate.