National Statuary Hall Collection Policy Act This bill establishes an additional requirement for the replacement of a statue in National Statuary Hall. Currently, a state's request to replace a statue it has provided for display shall only be considered if (1) the request has been approved by the legislature and the governor of the state, and (2) the statue to be replaced has been displayed in the U.S. Capitol for at least 10 years as of the time the request is made. The bill adds the requirement that at least two-thirds of the Members of Congress who represent a requesting state approve any request to replace a statue in National Statuary Hall.