A spot-the-difference game, where you compare a photo of a crime scene with one from before it was a crime scene, and every detail you find is a potential clue to solving the murder.
The game is played in real-time, and most levels have a time-limit of some sort: Certain evidence might erode or be destroyed, or the perpetrator might escape.
You have a partner/trainee whom you can task with following up on any given piece of evidence, but these tasks take time and you won’t have enough time to have them investigate everything. While present, they will also help observe the scene so you don’t get stuck.
(This photo’s from a PBS spot-the-difference game for Sherlock, but falls back on the meaningless observation of the genre.)
Cut-scenes and/or mini-games show what happens outside the crime scene.
Ideally, there's a natural text engine so that you can type questions and suspicions for your colleagues and suspects/witnesses you interview, but that might be technically prohibitive.