Some police cars may have and use run flat tires on their police vehicles.
However around here the police cars use regular tires that are designed for high speed pursuits.
The most common brand of tires that police here use are Goodyear and Bridgestone tires that are designed for higher speeds than a normal driver would be driving.
The tires that Police cars use are more rugged and can hold up better than normal tires.
I have heard that some police departments use run flat tires on their police vehicles but not all of them do or at least didn't the last time I worked in a police repair shop.
I used to change tires out on police cars and other police vehicles and Goodyear is what we mostly installed and they were just better built tires but not run flats.