They had several, overlapping groups that did domestic police and security stuff which you could sort of equate with modern SWAT teams, but nothing exactly like SWAT.
The first was the Gestapo, “Geheim Staatspolizei” or “secret police.” The Gestapo was noted for doing all manner of surveillance and snooping, but they broke down more than a few doors in military get-up in their days to act on information.
The SD, in later days, was sorta-kinda an up-weaponed police force. But... I can’t see as much similarity to SWAT units in that the SD (and later units build off the SD) wasn’t ever really responsible for domestic law enforcement.
Then there were the SS Polezei, the SS Police, which came about when the “Green Police” (known in German as “Ordnungpolizei” or “order police”) were sucked into the SS. Before ‘39, the Ordnungpolizei did what you’d expect normal civilian police to do - domestic crime enforcement, cats up trees, public safety, etc.
After ‘39 or so, the Ordnungpolizei (or “Orpo” for short in German) were sucked into the SS, and then the Orpo acquired para-military units known as “SS Polizei Bataillione” and these yahoos would do about what SWAT does today: Dress up like infantry, but not see actual battle. Instead, they worked on terrorizing the population with various door-to-door raids, looking for pesky Jews who might be resisting the grand plans of the Nazi intellectuals, etc.
I’d count the SS Polizei Bataillione as the closest thing to modern SWAT, mostly because of the military light arms and uniforms (including the coal-scuttle helmets), but never seeing actual combat. That comes pretty close to describing SWAT teams today: Lots of donut-munchers playing dress-up.
The Waffen SS was a personal infantry and mechanized infantry force of Hitler’s, and they weren’t really involved in any police work. They did for-real military engagements and killing on the front lines, often as shock troops who were sworn to die before retreating.
Thanks for the info!