Bafflement

"The key is to commit crimes so confusing that police feel too stupid to even write a crime report about them." -- Randy K. Milholland

Write from the investigator's point of view as he or she stumbles over clues that mean something but baffle the detective with their seeming illogic or chaos.

Detectives usually appear in contemporary fiction but don't be trapped by that. Create a fantasy detective. Is there magic in the world? Other races? A race that's always making fun of the intelligence of the detective's race and it's clear the member of the "superior" race is making fun of the detective.

Or set it in the future, with future technology. Is the detective less savvy about technology? Perhaps from a backward colony, or less sophisticated race. Is the crime on the detective's home planet committed by an alien or is the detective the alien called in because the clues seem targeted at the detective's people.

Or set it in some historical time. Mongols? Samurai? Inuit? Buddha?