Police automatically have immunity for acts within their assigned responsibility. It’s called qualified immunity.
I was a cop. I’m fully versed on Qualified Immunity.
It covers that if they’re doing their jobs according to the law, then they are immune from civil actions. If, during the event, they broke the law, then they can be sued and also charged with a crime.
If a law enforcement official says that he’ll only answer a question if he’s given immunity, that should be raising a tsunami of questions as to what happened.