Just a little story...
When I lived in San Diego during the 80's a cop was murdering women. On duty working nights, the cop would pull women drivers over, guide them onto a road leading to an underpass (dark and secluded) then would rape and murder them. This was just north of the city, off the freeway in a fairly secluded area. It took investigators some time to figure out who was killing the women because naturally they never suspected this cop.
Another hard to solve crime I thought was peculiarly interesting was when an on duty police officer was found shot dead in his cruiser. The officer dead, discovered parked in a small secluded road-side park. I knew that park. People working in the area would drive and have lunch in that park. What was strange, there was no evidence of any confrontation or anything out of the normal. Just a police officer found shot dead sitting in his car. Eventually resolved, what happened was another police officer who also covered the same area had went on vacation. His cruiser parked at home while he and his wife were gone on vacation, their teen age kid and his buddies decided to take dads police cruiser out driving and have some fun. When they just happened to pulled off the road into this same road-side park they discovered yet another police cruiser stationed in the park on his rounds. The officer recognized the other cruiser as it pulled into the park and thought it was an officer that he knew with recognizing the cruiser markings. The teens in old dads cruiser knew they were busted big time, they panicked, and shot the officer on the spot. The officer probably never knew what hit him or that kids were in the other police cruiser. It took some time before investigators determined it was the kid of a cop in old dads police cruiser that committed the murder. Someones going to get grounded, for life.
Just my 2 cents worth.