No, you are correct. But the Capitol is in DC, and crowds outside the Capitol are in DC. I'd have to see a map to be certain, but I would imagine for any large gathering, sufficient forces may be needed the Capitol and in surrounding areas.

To your point, though:

> D.C. Metropolitan Police Department would be the lead agency and would coordinate with the Capitol Police, the U.S. Park Police and the U.S. Secret Service.

It appears the Mayor had been requesting assistance from federal agencies in the week leading up to ceremony, but declined additional assistance greater than a force of 340[0], likely to avoid having images like this one[1] giving the impression of military being involved in the election process.

[0]https://www.npr.org/sections/congress-electoral-college-tall...

[1]https://pbs.twimg.com/media/ErEvfgnXAAA2kEc.jpg

Capitol Police are federal, not DC police