Features two detectives, Ranma (who is pretty much Jim Rockford) and Rella, who end up sharing the same body and swapping places at midnight (at least in the anime and the 1982 version of the manga). The gimmick is that one tends to find themselves in the middle of the case the other is involved with and so has to unravel the case without knowing the beginning of it.

2007′s Skull Man adaptation is a detective show for much of it’s run – rather than focus on Skull Man as the hero, it focuses on a journalist and photographer’s attempts to figure out who Skull Man is and what is going on in the town. Only once Skull Man is revealed in the final quarter of the series does it shift to action.

I’d class Mononoke as an occult detective show as the focus is on The Medicine Seller’s attempts to deduce the Form, Truth and Regret of the individual mononoke, rather just tell a ghost or folklore tale.

And a couple of shows I’m only aware of rather than seen:

Dr Fabre Is A Detective – a 2000 show that I have little on beyond it’s existence and Enoki Films’ page on it http://www.enokifilmsusa.com/library/fabre.htm

St. Luminous Mission High School – 1998 mix of mystery and harem as the only boy at an all girls school investigates mysterious goings on.

Gunsmith Cats also has a bit of detective work in there as a common theme.

If Paprika counts, this one should.