Is this an actual thing? Psychics being consulted in police investigations, I mean?
It is in the US. The Justice Department even has guidelines for the use of psychics in law enforcement. It consulted with some 11 police agencies, and reported that the majority favour consulting psychics as soon as a case was seen to be difficult or unusual (over the more conservative path of holding back until all other avenues had been tried without success) – because that would help them decide whether to narrow down or widen the scope of the investigation. I suspect though, that they have a very, very short list of go-to psychics they’d rather use, who are tried and true and know the kind of detailed info the cops require Vs the 400-500 psychic strangers who hound them on every case with vague descriptions of everything and anything.
It's certainly a thing in TV shows.
I’ve just watched a Portuguese talk show on YT that’s a few years old, about the Maddie McCann case. ….After the show hostess had screened a short clip from another Portuguese show that had featured 2 male Canadian psychics trying to locate Maddie’s remains, she remarked that Portugal didn’t use psychics, they relied on facts. She made a point of it: that the use of mediums was uncommon on the continent, but not in Anglo-Saxon countries. ….Her guest on the show was Gonçalo Amaral, the retired Portuguese police chief who’d been removed as lead investigator in the case. He revealed that the FBI had been very keen to assist in the case (but hadn’t because of the prior involvement of British police). Apparently, the very first form of assistance the FBI had offered was the services of a female psychic!
Edited to add: Apparently the US law enforcement agencies tend to prefer women psychics.