We did have LE involved for awhile. The CIC-Counter Intelligence Corps had LE powers. I had a link to a declassified paper which describes their mission in detail but the link went bad will try again later.
Also for a short time we actually had an SF MP Company or Battalion, I think John T. Fishel knows about them.
Here is the Link. CIC In WW2 Mission and History.
http://www.fas.org/irp/agency/army/cic.pdf
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