Lemme see if I can get this straight.
Procedures have since been changed last fall because of the inefficiency of the bureaucracy.
If POTUS orders the Guard, end of story.
Otherwise, the Capitol Police Chief of Police, Steven Sund, would request the Guard thru the House and Senate sergeants-at-arms.
The sergeants-at-arms would request approval from the Capitol Police Board, which is comprised of the 2 sergeants-at-arms and the Capitol Architect.
The sergeants-at-arms were under the direction of Pelosi and McConnell in Jan 2021.
"Capitol Police Chief Sund asks the House and Senate sergeant-at-arms about the possibility of placing the D.C. National Guard on standby, in case the Capitol Police needed quick backup. In an interview with the Washington Post published on Jan. 10, Sund says they were hesitant to agree. According to the article, “House Sergeant at Arms Paul Irving said he wasn’t comfortable with the ‘optics’ of formally declaring an emergency ahead of the demonstration, Sund said. Meanwhile, Senate Sergeant at Arms Michael Stenger suggested that Sund should informally seek out his Guard contacts, asking them to ‘lean forward’ and be on alert in case Capitol Police needed their help.” All three officials — Sund, Irving and Stenger — have since resigned.
Update, Jan. 28: In prepared testimony for her Jan. 26 appearance before a closed session of the House Appropriations Committee – which was obtained by the New York Times — the acting chief of the Capitol Police, Yogananda D. Pittman, confirmed that on Jan. 4 – two days before the riot – “Sund requested that the Capitol Police Board declare a state of emergency and authorize a request to secure National Guard support. The Board denied the request, but encouraged Chief Sund to contact the DC National Guard to determine how many Guardsman could be sent to the Capitol on short notice, which he did.” The Capitol Police Board has three voting members: the House and Senate sergeants-at-arms and the architect of the Capitol. As we noted in our initial report, the House and Senate sergeants-at-arms have since resigned.
Jan. 5: According to the Pentagon, Mayor Bowser delivers a letter addressed to the U.S. acting attorney general, Miller and McCarthy confirming that there are no additional support requests from the D.C. National Guard. Bowser later says that she already had the support she requested from the National Guard and that any decision to request guard forces to protect the Capitol is not hers. “The Capitol Police and the leadership at the Capitol, they did not make the decision to call in guard support,” Bowser later says in a press conference on Jan. 7. “I cannot order the Army, the National Guard, to the United States Capitol grounds. I can, in the district, with the approval of the secretary of the Army.”
https://www.factcheck.org/2021/01/timeline-of-national-guard-deployment-to-capitol/