American forces can be arrested by civpol, but are usually dealt with by their own authorities under the auspices of The Visiting Forces Act. This even covers capital crimes, such as murder, rape and Arson.
You're obvioulsy unfamiliar with the 'Sevice Personnel Immunity From Any Wrongdoing Act 1923' then Constable?
May I draw your attention to s.1, which states 'A person is not guilty of any offence whatsoever, despite his conduct or state of sobriety, if he is the rightful keeper of an MOD F 90, whether in possession of said document at the material time, or not, and 'squaddie', 'barrack room lawyer' and 'arsewipe' shall be construed accordingly.'
When the young Welsh soldier died from a 'beasting' he happened to die in Salisbury General Hospital which meant that the Service Police had no jurisdiction over the case and Wiltshire Constabulary dealt with it throughout.
The Deepcut deaths were dealt with by the Service Police as they occued on MOD property, so that leads me to believe that the actual location of the event seems to decide who has jurisdiction. I may be wrong though.
In Salisbury young squaddies are arrested for fighting and being overly drunk every single weekend. The RMP are usually in the centre on Friday and Saturday nights and the police are happy to hand them over for the following reasons:
a. They do not have to go back to the station and fill out mounds of paperwork.
b. They can remain in the centre for further trouble and their numbers are not diminished (along with a vehicle)
c. The army punishment will be harsher than the 'bound over to keep the peace' they would get from the local magistrates.
The service police and constabulary work well together in salisbury.