Tribal Police Department Parity Act This bill treats tribal law enforcement agencies in the same manner as federal, state, and local law enforcement agencies for purposes of accessing firearms. The National Firearms Act (NFA) generally imposes a tax on the transfer of an NFA firearm; however, specified governmental entities (e.g., federal, state, and local law enforcement agencies) are exempt from this transfer tax. This bill extends this exemption to Indian tribes (and consequently, to tribal law enforcement agencies). The Gun Control Act (GCA) generally prohibits the interstate shipment of firearms to unlicensed persons, but exempts specified governmental entities from this prohibition. This bill makes Indian tribes (and consequently, tribal law enforcement agencies) eligible to receive firearms interstate. The GCA also prohibits the transfer or possession of machine guns manufactured after 1986, but exempts specified governmental entities from this prohibition. This bill makes Indian tribes (and consequently, tribal law enforcement agencies) eligible to transfer or possess these machine guns.