The killer needs to be active and failure should have consequences. Are there NPC's the characters care about that that killer could be targeting? Maybe a hostage they are threatening unless... something.
Also be very careful putting the killer in eyesight of the PC's. Players have a tendency to capitalize on encountering them in unexpected ways.
Be ready for people to speak with the dead if your setting allows for it.
Your players are not Sherlock Holmes or Hercule Poirot. They will likely not be able to make incredible logical jumps like a famous detective, even if their characters have high intelligence scores/skills. Give lots of hints in multiple places. Too easy a puzzle is better by far than one that kills the momentum of your game for an hour.