One thing to add to what others have said but when the feds show up they don't just take over an investigation in real life. They always show in TV/Movies about feds coming and taking over but it isn't true.
In reality the FBI shows up and HELPS local/state police. They pool their efforts together. They work together. They don't just take over an investigation and leave the local/state police to do nothing. Local/state police are not subordinates to the FBI and the FBI does not supervise or take over investigations.