Nonpartisan Postmaster General Act This bill restricts the political activities of the members of the Postal Service Board of Governors, including the Postmaster General and the Deputy Postmaster General. Specifically, the bill (1) prohibits the Postmaster General and the Deputy Postmaster General from taking an active part in political management or political campaigns; (2) prohibits the Board of Governors, the Postmaster General, and the Deputy Postmaster General from holding any political position while in office or soliciting funds for the campaign of a candidate for elected office or for a political party; and (3) restricts nominees for Postmaster General and Deputy Postmaster General to those who have not engaged in political activities in the four years prior to their appointments.