Ok, after some googling, I finally remembered the name. It's A Festival of Skeletons, by RK Astruc and Kay T. Holt.
When Kamphor's west end sees a series of prostitutes murdered, its
citizens are fearful that a serial killer known as the Knife has
returned. But the mortician Sink, owner of Kamphor's finest morgue,
doesn't believe that the Knife has resumed killing - and he'd prove
it, if his former student and current hateful rival Damien Torvault
wasn't getting in the way.
Sink and his two apprentices, handsome-if-loony Joshua Finkle and
merkind Vona Urgarth, investigate the murders on their own. Sink's
ability to tell exactly when and how a person will die just by
touching them earns him no friends, but it does yield some interesting
clues - as does Sink's other gift. The one which incites him to wear
The investigation is further complicated when Joshua's time is taken
up running a 15-Step program, and Vona becomes intrigued by a
repugnant yet strangely irresistible cook. Even Sink's next-door
neighbor, Policewoman Arifia Fowles, seems hell-bent on not just
hindering Sink but arresting him, regardless of a crime.