National Commission to Investigate the January 6 Attack on the United States Capitol Complex Act This bill establishes in the legislative branch the National Commission to Investigate the January 6 Attack on the United States Capitol Complex. The commission must (1) conduct an investigation of the relevant facts and circumstances relating to the attack on the Capitol; (2) identify, review, and evaluate the causes of and the lessons learned from this attack; and (3) submit specified reports containing findings, conclusions, and recommendations to improve the detection, prevention, preparedness for, and response to targeted violence and domestic terrorism and improve the security posture of the U.S. Capitol Complex. The bill gives the commission specified powers, including the authority to hold hearings, receive evidence, and issue subpoenas. The bill also provides for the composition of the commission and the appointment of staff, and it requires the commission to hold public hearings and meetings to the extent that it is appropriate. The commission must also release public versions of its reports.