I would suggest Spice and Wolf, even though it has nothing to do with crime.

Going to recommend Rozen Maiden, although it's not a crime drama.

Witch Hunter Robin or S-Cry-Ed

A couple of movies?

Kiki's Delivery Service and My Neighbor Totoro.

Thet aren't Death-notish, and they aren't a series, but if you don't like them you have a heart of stone. STONE!

Was going to recommend Puella Magi Madoka Magica but then I saw legal.

Hellsing: Ultimate

Assuming, of course, that blood/gore isn't a deal breaker. I mean, the main character is Vlad Dracula.