Fingerprints, hair or clothing samples, asking nearby drone hobbyists if they might know anyone into drones who might want to murder the victim, sales records of retailers of drones or drone supplies, and of course the normal stuff, like who would want the victim killed in the first place.
I'm not a detective, but I suspect having the large, complex piece of electronic equipment that was used as the weapon would be a godsend compared to the evidence available in a normal murder or assassination investigation.
Obviously the plan wouldn't be "drop the drone at the scene of the crime". Why would anyone ever do that? I mean, of course they would minimize the reveal were that to happen (though note that drones are becoming absolutely pedestrian, so this notion that you talk to the niche club and find the drone enthusiast is absurd), but the rational plan would be that the drone would escape as well. Because its odds of escape, currently, barring mechanical defect, would be close to 100%. No one is going to catch a drone.
I'm not a detective, but I suspect having the large, complex piece of electronic equipment that was used as the weapon would be a godsend compared to the evidence available in a normal murder or assassination investigation.