I would guess in some sort of auto service bay, preferably one with oil changing facilities.
You do realize that there is more than one police department in the world, right?
They go to the City garage.
Where I live there is a service center which services all government vehicles. This is includes but not limited to, police cars, fire trucks, sweepers, forklifts, community center vans and buses, water trucks, backhoes, dump trucks, tractors, golf carts, and dually trucks.
It depends on the department. Some large departments have their own shop.
The town where I grew up informs that county Sheriff that the ONLY patrol car will be out of service while they take the car to the local mechanic.
Larger police forces have their own dedicated workshops who carry out maintenance and repairs of their vehicles.
Smaller police forces will use normal garages, usually under contract; or may pool their resources with neighbouring forces to run a police workshop.
Clearly it depends on where you are and the size of the fleet. We have our own police workshop where they do servicing, repairs, updates etc. on the cars, vans, bikes and motorcycles. Body repairs are usually farmed out to a local body shop.
A long time ago I lived in a very isolated location where there was one police car, one fire truck and one ambulance. The mechanic at the fire station dealt with all of them.
Where I live they have a central county maintenance facility to service all the cop cars, snow plows, etc.
I don't know if it is still the case, but when my dad worked at a local Ford dealership about a decade ago, they would work on the police vehicles for the city.
The dealer who sold the fleet to the city usually does that. The Oakland Police Department has their SUV's serviced at Albany Ford where the fleet contract was done.
Larger departments might have their own shops for vehicle maintenance.
Where I live, I often see police cars parked at a local mechanic / gas station: I guess the township contracts them to do maintenance.
oil change place
they have thier own pumps for oil.
The Police Department I worked for was large enough to have its own maintenance facilities.
the departments have their own mechanics or they send the cars to an outside mechanic they have a contract with.
I've seen NYS State Police car's having their oil changes done by local private mechanics.
most police departments have their own mechanic who does basic maintenance on them. some contract out to repair shops like mine for bigger jobs
At there government workshops
Police vehicles have a workshop
It all depends on where. For example, where I live, which is a city of 30,000, all city-owned vehicles including police cars are maintained in house by a city run maintenance facility.
I live in a small town. A local garage has a contract with the City to perform the maintenance for police vehicles.
At the city they work in. I use to do a lot of work on cop cars and fire trucks in the Lewisville tx
In the garage.
In my area, the DPW garage always did it, but I see police cars at dealerships from time to time.
I never saw one at Jiffy Lube.
At the "motor pool", where they take care of all the cop cars.