I worked at a small school that had diesel for the buses but vans had to be fueled at a gas station with a school credit card. Police departments in any major (American) city will definitely have several fueling stations for cop cars.
It depends on where you live, but a lot of large US cities have their own fueling stations. That way, the city can buy fuel by the tanker load and avoid gas taxes.
It’s both. Tax exempt paperwork is annoying, and one of the best ways to minimize it is to minimize the number of purchases that you make. Buy in bulk when you can, because one large purchase is less likely to have an error (or at least, more likely to be noticed) than a hundred small purchases.
In my rural county the cops, school busses and basically all the public service vehicles like ambulances and plows fill up at the farmer's coop, where farmers get cheap gas for their tractors. I have heard that this is not technically legal, because that has is specifically for tractors and has some kind of special price because of that, but I don't know if that's true or not. I know you're not allowed to fill up your regular car there, but some of the farmer's and cops do.
I think this is usually specifically for diesel fuel. Certain places have diesel fuel with red dye in it that is tax exempt. Any fuel you buy from a standard gas station has a good amount of tax baked into the price and it's earmarked to go towards road and infrastructure repair. The thought process is, if you're not using said vehicle on the road, you shouldn't have to pay this tax.
So, they dye it red, sell it only at special places, and you get fined pretty heavily if you're found using it in street vehicles. Typically it's truckers that do it because most American cars (including cop cars) are not diesel. And I've never heard of this setup for regular gas.
My father used to repair gas pumps for a living. I went out with him on a few jobs. You'd be amazed how many large facilities that have their own fleet of cars end up setting up their own gas station. Universities, large hospitals, movie sets, and of course emergency vehicles.
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.
If you're serious, I would assume that it's not that hard to red-flag cases where fuel mileage drops after you have used the vehicle, as well as before. After it's happened a couple of times, should be able to identify the cause.
Back when I worked IT for the city we actually got a tour of the main police station. There was a gas pump on sight where officers could make sure their car was full before and after patrols
Where I live (Germany) they usually have cards with which they can pay at most big gas stations. Kind of like a pin protected voucher card. They usually have a maximum limit though.
So when we operate a mobile gas station in catastrophic events like big wildfires etc. We usually have to get a limitless card, because otherwise we need a new card 3-4 times a day because we refill our 450 liter tank so often.
Most fire stations and probably police stations too have an emergency depot though. As does the city. Sometimes the city depot is shared with the depot of the public transport company though.
There's a station I use regularly that has to have some sort of commercial plan. I regularly see cop cars, UPS trucks, and one time a yellow cab filling up there.
I see the cops in my city, and a few nearby, at the gas station all the time. They all have gas cards. Some of the larger cities near me have pumps at a few of the city properties that the city employees can use to fill up city vehicles.
I work in a petrol station and I’ve had police and ambulance crews come in for fuel, a bus even pulled in with passengers still on board last Saturday. Never seen a fire engine pull in though but I’d guess they have tanks in the firehouse.
They maintain their own fueling depots around their jurisdiction. One of ours is down the block from a Walmart, on the back side rode without much other development.
They do this to get cost savings on the fuel, maintain a segregated supply for themselves in emergency, and to avoid being near us plebs in a vulnerable (unfueled) state.