United States Capitol Complex Security Improvement Act This bill establishes reporting requirements and other measures related to the January 6, 2021, attack on the U.S. Capitol. Specifically, the bill requires the U.S. Capitol Police (USCP) to investigate and report on (1) intelligence failures related to the attack, and (2) the use of de-escalation strategies by the USCP during the attack. In addition, the USCP must (1) assess the feasibility and desirability of establishing a nexus for sharing intelligence with other law enforcement agencies and appropriate federal officials, and (2) carry out an initiative that improves its ability to respond to riots. Further, the Architect of the Capitol (AOC) must assess the damages caused by the attack. The bill also requires the AOC to remove any remaining perimeter fencing that was installed around the Capitol in January 2021, and it prohibits the AOC from installing any such fencing in the future unless at least three members of the USCP board approve the installation. The bill places the Librarian of Congress on the USCP board.