If this is about the story you posted in SYW, in which the murder was committed in New York City, the murder would be investigated by the NYPD. Fortunately, they have the best homicide detectives in the world. The assassination of a foreign head of state would have dozens of detectives working it.
The FBI would manage to insert themselves into the investigation, of course. Their access to resources (money and personnel) would be a good complement to the NYC detectives, but the two agencies don't get along. The situation is exacerbated by the current police commissioner and his staff, none of whom have much use for the feds.
The most likely scenario would involve a multi-agency task force, composed of the New York City Police Department, the Federal Bureau of Investigation, the Diplomatic Security Service, the United States Secret Service, the New York State Police, Scotland Yard, and whatever other agencies are responsible for any jurisdiction to which the investigation leads. The could concievably wind up being sevwral hundred investigators, broken up into numerous smaller teams whose actvities would be coordinated out of the Commissioner's office at One Police Plaza. Teams would be assigned leads based on authority, expertise, and jurisdiction.