While federal agencies have resident agents in local police departments, the agents perform the tasks of the agencies- such as Secret Service for counterfeiting cases. The FBI does not investigate homicides unless they are of a significant nature, such as a serial killer or murder for hire.
Despite what is shown in the series, Michigan law does not require a license plate on the front of vehicles. Only a license plate in the rear is required.
The FBI resident agency that covers Battle Creek, Michigan is 27 miles away in Portage.