Immunity is a judicial construct in the first place, in the US - could be modified by a statute, and is, in parts of the US (Colorado). US and AUS are both derived from Brit Common law (except Lousiana is derived from French civil law).
I figure the two jurisdictions (US by and large, vs. AUS) are similar, but not identically worded.
Quick peek at AUS, it’s called “police immunity” there, and appears to derive from statutes.
http://www5.austlii.edu.au/au/journals/UNSWLawJl/2018/24.html
That which is given, can be taken.
But, sumthin’ ain’t kosher in Denmark if the head police dude is asking for this.