It's not a complete match, but as I noted above, there are some similarities to Philip K. Dick's "The Unreconstructed M" as per evidence matching robot on murder scene. It can be read here.
The small machine sneaks into an apartment and leaves behind a single follicle of human hair, two small grains of tobacco, and other small pieces of evidence. It then destroys a video recorder. A man enters the apartment and the machine shoots him in the head with an explosive pellet. The machine drops a few more items and hides by turning into a portable TV set as some people came in responding to the shot. They wonder where the murderer has gone. He came in through the window, it is clear, but how did he escape?
It is indeed set in a future time when data tracking and automated evidence collection have largely supplanted detective work, with part of the conceit of the story being that, as each bit of evidence is entered into the system, they narrow down their list of subjects.
Readers will right away notice the comparison between this story and “The Minority Report” written not long before. While we do not have the operation of Precrime in “The Unreconstructed M” we do have a criminal justice system that had done away with the need for the detective. A computer has taken over the job of solving crime. All the investigators need to do is put in enough data to eliminate all but one person from the list of suspects. Importantly, every time a crime is committed, we are all suspects. We are required to prove our innocence. The aggregated of circumstantial evidence is enough to convict. Also like “The Minority Report” we have a police officer forced into a dilemma of either exposing a fault in system that he relies on for his entire identity. Thanks to Beam’s old fashioned investigative abilities, Ackers learns that his system failed and that David Lantano was framed. In a twist, the ending seems to suggest that Lantano may have framed himself and his competitor Paul Tirol at the same time. He framed himself for the murder and framed Tirol for the frame job. This ensures his dominance over the industry. In the end, this matters less than what Dick is trying to tell us about the criminal justice system. As with “The Minority Report” we learn that no matter how perfect the system seems to be, there are flaws that can be exploited.
Not matching, they know who the murder victim is, and the intent is not to overthrow the system (although it looks for a bit like it is, and there's a side character who is suspiciously firm about abolishment of the system, but turns out to be a red herring), but to frame someone for murder, with it turning out that there's a second frame going on to make it look like someone is trying to frame another person for murder, complicated by a marital tiff.