story about a mind-reading private investigator who thwarts an alien invasion

Question

Trying to remember a book, perhaps a short story later developed into a book, about a mind-reading private investigator who thwarts an alien invasion.

The hook of it is a scene at beginning where he's investigating a disappearance/kidnapping/murder and he's tracking down a possible person of interest but shoots them on sight and it is only revealed later that he saw inside his/her mind and what he saw wasn't human. The invasion started with the secret return to Earth of human astronauts that had become possessed by the aliens. The authorities work with the detective to track down the remaining doppelgangers.

Answer 1

Possibly Three to Conquer by Eric Frank Russell

"Call Him Dead" is much less well known: it was serialized in Astounding in 1955, and published in book form the next year as Three to Conquer. It's about a secretly telepathic man who has on occasion used his abilities to help the police and the FBI solve crimes. One day he "hears" a man dying -- after going to try to help the man, a state trooper, unwillingly he again becomes involved in investigating a crime. It turns out that the criminals are something quite different -- for one thing, they can detect our hero when he "probes" their mind.

Though the above review above is coy about what's going on, the villains are parasitic aliens who infested returning astronauts as this review makes clear