Capitol Police Emergency Assistance Act of 2021 This bill allows the chief of the U.S. Capitol Police to request emergency assistance from executive departments and executive agencies to prevent significant disruption of governmental function and public order at the U.S. Capitol. The bill also eliminates statutory qualification and approval requirements for law enforcement and uniformed service personnel appointed to serve as special police officers, including during periods of emergency initiated by the chief under the bill. Further, special police regulations prescribed by the U.S. Capitol Police Board are subject to approval by the Speaker of the House and Senate majority leader under the bill. Those regulations are subject to approval by the Speaker and the President pro tempore of the Senate under current law. Finally, the bill requires the Senate Committee on Rules and Administration and the House Committee on House Administration to jointly conduct at least one oversight hearing of the U.S. Capitol Police Board during each Congress.