The Soviet NKVD, Nazi German SS, and Imperial Japanese Kempeitai all had full combat divisions that fought on the battlefield
Why did totalitarian governments recruit secret police as full combat divisions fighting on the frontlines?
The SS was not a police force, though it controlled police forces through the RSHA.
It was however the "private army" of the Nazi Party, and provided a counterweight to the Wehrmacht, which was not regarded as reliably loyal to the regime. It was also a vehicle for the military ambitions of the Nazis and Hitler, in particular the idea that true-believing Nazis were better soldiers.
The NKVD was a police force; it contained combat troops because the Party always feared a military coup and wanted an absolutely loyal force to suppress any such plots. (The Soviets were much more paranoid than Hitler.) Also the NKVD troops could be trusted with special weapons, such as the first Katyusha rocket batteries. And they were used to enforce discipline against regular army troops when necessary. (The SS was also used this way toward the end of the war, but in a clumsy manner. I have read that near the end, it was dangerous to be sent as a messenger to HQ, because SS vigilantes were summarily hanging anyone moving to the rear as deserters.)
I've never heard of Kempeitai combat units.
Italy also had "party" units of "Young Fascists" and "Blackshirts" - not associated with the police, but as with the SS, meant to demonstrate the prowess of true believers.