UK police have had various types of Jaguar over the years; there was a period where the original Mark 2 Jag could outrun the police, so they had to buy some as well. The Mark 2 became ubiquitous in police procedural TV shows, usually driven by criminals, but also Inspector Morse.
In Italy the Carabinieri[0] used to have a Ferrari 250 GTE 2+2 in the '60s. The car is still around[1] and is legally allowed to go around with the original "police colors" even tho it's now owned by a private collector.
There's plenty more modern sport cars these days, in various countries.
the state of Austria usually buys its police cars from Porsche (the dealer not the carmaker) guess, that doesn't count. but Austria had Porsches (some of them 911) in the 60s
For the present day: https://www.selectcarleasing.co.uk/news/article/most-powerfu... (fun use of FOIA)
https://policepathfinder.com/what-car-do-british-police-use/