One of my better and more lucid fans wrote to tell me that the FBI investigates Police officer deaths. Not really. Only in cases where the Federal government is also investigating for corruption cases. In the case of Chicago, the feds would be involved only to insure that the rights of the accused were not abridged.
The Illinois State Police would be tasked with supporting the initial investigation. But local homicide would be deeply involved. Hmm?
And the worst thing that could possibly happen is to have a decorated investigator perform this as her Last Case.