Protecting the Rights Of Towns against federal Enforcement contrary to Constitutional Tenets for Immigration Act or the PROTECT Immigration Act This bill establishes that the authority to investigate, apprehend, or detain aliens for the purposes of immigration enforcement is limited to immigration officers and authorized Department of Homeland Security employees, except when such authority is provided to other individuals under specified statutes. Specifically, this restriction does not apply in certain instances involving (1) an actual or imminent mass influx of aliens, (2) persons bringing in and harboring aliens in violation of immigration laws, or (3) an alien illegally present in the United States who had previously left or was deported after being convicted of a felony. The bill repeals the authority allowing the Department of Justice to enter into agreements authorizing state or local government employees to perform immigration enforcement functions.