I don't know about the State Troopers, but I think that the Orange County Sheriff's Department is the law enforcement of choice at WDW. I am not aware of what authority the in-house security has, but I think that they can detain for a while and then either have to release or call in the Sheriff's.
Funny the things you learn when taking the Keys to the Kingdom tour..... Disney Security are cast members who have been "cast" in that role and the uniform is a costume which has been designed to look like security. Disney security are NOT law enforcement officers. If someone needs to be arrested, then Security CM will detain them until Orange County sheriffs show up to arrest and remove the individual. Disney Security can escort, or attempt to escort, a guest from the park, but they have no arrest authority.