Typically a case like this, multiple serious felonies committed in multiple states by the same individual, would fall under federal law enforcement jurisdiction. In this case, a serial rapist striking in over a dozen states, would be investigated by the FBI's National Center of the Analysis of Violent Crime (NCAVC) unit, they would take the lead on the case with assistance from local law enforcement as needed. This is typically done because law enforcement agencies' don't always work well with other departments and even when they do it can be very complicated coordinating everything and then figuring out who gets to try the suspect first. So instead of multiple agencies running their own investigations and multiple prosecutors trying to try the same suspect the FBI leads the investigation and the suspect is tried in federal court for all the crimes he committed, instead of being tried in one state at a time for each separate crime.