If your wife wants to try one with a literal ghostly detective, Lee Killough's
Killer Karma is about a cop who has to solve his own murder. It was offered free
some time ago by the author/publisher who might repeat it at some point. And you can always check to see if you might like her writing by downloading her
current freebie which has a vampire cop.
Disclaimer: I have not read either, nor any other works from this author. But other MR members have stated that they enjoy her stuff and were happy to see it offered free.
ETA: There's also a freebie short story for the Jack Nightingale series mentioned upthread,
available on Amazon UK.