Protecting the Rights Of Towns against federal Eforcement contrary to Constitutional Tenets for Immigration Act of 2017 or the PROTECT Immigration Act of 2017 This bill amends the Immigration and Nationality Act to provide that the authority to inquire about or verify immigration or citizenship status and to investigate, apprehend, arrest, or detain an individual for a violation of such Act is restricted to immigration officers and authorized employees of the Department of Homeland Security (DHS) and subject to limits set forth in other provisions of law. DHS authority to enter into written agreements with a state or state subdivision to perform immigration-related investigations, apprehensions, or detentions of aliens in the United States is eliminated. The bill exempts from the restriction under this bill DOJ authority to enter into other state and local agreements: (1) in the event of an actual or imminent mass influx of aliens representing urgent circumstances; and (2) with respect to immigration-related detentions in non-federal facilities, including personnel and facilities construction. The bill also exempts from such restriction state and local enforcement authority to arrest and detain certain previously-deported illegal aliens who have been convicted of a felony.