Reader Bill has brought some further specific statutes to my attention with regard to the jurisdiction and operations of the US Capitol Police. None of what follows comes as any surprise to me--and it shouldn't to anyone else, either. The provisions in these laws are typical for federal LE agencies--providing for deployment outside normal jurisdiction and for receiving military equipment.
The section that covers deployment outside normal jurisdiction is to prevent conflicts and screwups--even though the USCP already has national jurisdiction for matters within their authority. This provision is a safeguard measure.
Re "surplus or obsolete property", that mostly allows LE agencies to receive and use military equipment. YMMV in that regard. I'm one of those people who deplore the militarization of LE at all levels throughout the land, but provisions of this sort are pretty typical since even before the GWOT began.
First, here's the overall Chapter of the US Code that covers the USCP: