If a US Senator was assassinated who would investigate his death? The local police? The FBI? The Secret Service?
Hmm who was the last assassinated US Senator?
The only ones I can find are Bobby Kennedy and Huey Long. Kennedy’s assassination was handled by LAPD and the Secret Service/FBI. My guess is any major government official who gets killed is going to be the caseload of Homeland Security these days, which means a veritable alphabet soup of agencies, with the FBI taking point.
I doubt there’s a simple answer to this, because at least it would depend on how and why the senator was killed. The local police would definitely be involved if they were killed in their private residence by a relative, but the FBI might still check for any connections with the senators official business. For that matter, being killed by a known international terrorist might involve the CIA.
I don’t think the secret service would normally be involved for a senator, but counterfeiting is under their jurisdiction, so murder by a counterfeiter could involve them, too.
ETA: I should have thought of a senator running for president for the secret service.
Well I need this for a story I’m writing and in my story I’m positing that the body is found in the mountains where the Senator was hiking.
Oh well in that case clearly the Argentinian police would be involved in the investigation. 
18 USC 351
It’s a federal crime, so the FBI would take charge, unless the senator happened to be under Secret Service protection.
The law was enacted in 1971, so RFK’s assasination was a state crime.
For the story, I think it would depend on whether the discoverer knew the guy was a Senator or not. The sequence of events would surely begin with dialing 911, and then the local cops coming to the scene. Then it depends if THEY recognize him as a Senator. Your story would weave all sorts of ways with this.
ETA: For example, the FBI might discover it from some agent seeing a CNN viewer phone cam during a live broadcast.
If it happened on Capitol Hill (although I know it won’t, given the story you have in mind), the U.S. Capitol Police would be involved from the outset.
Well the Senator goes missing and the people who find his body are cops or FBI agents who are searching for him.
Well done sir, well done.
Both the FBI and local police would be involved; the FBI would head the investigation, as they always do, but depending on local facilities, a lot of the investigative work might be done by locals. If the guy’s just missing and there’s no immediate reason to suspect foul play until the body is found, then I would figure the FBI would have a smaller presence. Once it’s known to be a murder, they’d ramp up and take over.
The nice thing about writing fiction is that you don’t have to get these details exactly right as long as they sound right; the only readers who are going to care much are FBI agents, and they already have plenty of other poorly-researched media to worry about.
–Cliffy