"But isn't the military police solely in charge of the soldiers? How come they are directly in charge of the civilians?"
The conventional military police, also known as the military police, are primarily responsible for maintaining military discipline, ensuring the execution of military orders, and organizing military courts. They are truly policemen within the military. However, the Titans' military police are different; from the very beginning, this department has had incredibly vast powers. Even the lowest-ranking non-commissioned officers can arrest high-ranking officers adorned with medals.