This is a humorous mystery series by Kevin J. Anderson, who writes Dune and Star Wars stories as well.
The hero’s name is actually Chambeaux, not Shamble, but since he is a zombie, people just assume…. Dan has been murdered, only he didn’t die permanently. He came back as a zombie, and his girlfriend, also murdered (presumably by the same hand) is now a ghost. They’re still working though, both at his private investigator’s office, along with a living human lawyer who helps them out.
This is a fun read and I’m looking forward to finding out if Dan can solve his own murder (and that of his girlfriend, of course).