To Sketch a Thief by Sharon Pape.*
When PI Rory McCain returns a dog that wandered into her yard, she doesn't expect to find the mutt's owner, Brenda Hartley, dead in the middle of the kitchen floor. Not wanting Hobo to go to a shelter, she takes him home, much to the annoyance of her partner, the ghost of one-time US marshal Zeke Drummond. The antipathy goes both ways: Hobo is frightened of the spectral lawman.
Having been the person to find the body, Rory would like to search for the killer, but as a private investigator, she can't unless someone hires her to do it.
When a friend of Brenda's, a dog breeder named Tina Kovack, hires Rory to find the dead woman's other dog, a purebred Maltese that wasn't found at Brenda's house. Tina is certain that Tootsie, was stolen by the person who killed Brenda. Rory isn't sure if she agrees, but she takes the case, because it means that while she's searching for the dognapper(s), she can also hunt for Brenda's killer.
Zeke Drummond's spirit remains earthbound because he wants to know who killed him, and he is physically unable to investigate on his own. He is a non-threatening character, who just happens to be unable to manifest outside the house, although he's pretty good at doing internet searches.
Zeke's sensibilities are very 19th Century though, while Rory is very much a self-sufficient 21st Century woman, and they do clash over societal proprieties. As a result, there's more humor here than spookiness, and especially with the addition of Hobo, and Rory's sleuth-wannabe Aunt Helene.
*FTC Full Disclosure: Many thanks to the publisher, who sent me a copy of the book for review purposes.