While your question is dated, I thought I would respond in case you are still interested.  However, I do want to make a distinction in the use of terminolgy, MP Officer vice Military Policeman.  They are distinctly different.  I am a former officer whose "branch" was MP.  The amount of actual law enforcement (LE) I did was miniscule, and likely not even worthy of the classification LE by true LE professionals.  That being said, you DO NOT take any sort of polygraph for enlistment into the US Army Military Police Corps.  If you are commissioned as a Second Lieutenant (OCS, ROTC, USMA, etc.) you also DO NOT take a polygraph.  I will caveat my statement, in that for specific duty assignments as an officer or enlisted, a polygraph could be required depending on the location, description of duties and security classifications of the assignment.  Hope this helps and isn't too late.  v/r M6

If they research you for a TS clearance, they will find out. A kid got kicked out of my division in bootcamp for this reason. He needed a TS- C  and the background investigator found out he had seen a doctor about being bi-polar. He wasnt even offered a new rate. They kicked him straight out.

Military police officers serve many purposes. Not only are the military police responsible for keeping lawful order by performing duties like traffic checks and patrolling, but they also collect evidence and provide maneuver and mobility protection. Becoming a military police officer means that beyond serving and protecting, you will also have the responsibilities of a soldier as well.