The city has a private fuel station (or if it’s a large city, they may even have multiple fuel stations,) which they use for their entire fleet of cars. Not just police, but also all the random Parks pickup trucks, Traffic trucks, forklifts, generators, etc…

Even a mid-sized city will have hundreds of vehicles, so it’s easier for them to simply deal with the fuel providers directly. Instead of having to deal with tax-exempt paperwork every time a car needs fuel, they simply buy the fuel in bulk and refuel at the private fuel depots.

When I go to fuel a city car, it has a fob that gets scanned at the pump. This tells it which car I’m filling. Then I have to input the mileage, so it knows how far the car has driven since the last fill. Then I have to scan my city ID, so it knows who is filling the pump. Then finally, it will calculate the amount of fuel needed to fill up and stop pumping automatically once it reaches that; The same way you can put $20 on a pump and it’ll stop, the pump goes “this car gets 32MPG and has driven [x] miles, so it needs [x/32] gallons of gas.”

This is mostly to prevent fuel theft, because I can’t simply fob into the pump then keep the pump active after the car is full. Like I can’t fill the car then also fill up a gas can, because the pump has already turned itself off once the car is full.