Not sure if Park Police has jurisdiction over the Capitol grounds. I believe that is the jurisdiction of Capitol Police and possibly also DC Metro police.
The Park Police does have jurisdiction over the Capitol grounds and they were heavily involved in J6.
I am hesitant to give links because they seem to be left wing propaganda on J6.
Here is a neutral one on the duties of the Park Police:
https://www.nps.gov/subjects/uspp/jurisdiction-and-authority.htm
https://en.wikipedia.org/wiki/United_States_Park_Police
“In 1925, Congress placed the Park Police in the newly created Office of Public Buildings and Public Parks of the National Capital.”