Parity for Tribal Law Enforcement Act This bill treats certain tribal law enforcement officers as federal law enforcement officers under specified circumstances. Specifically, the bill authorizes the law enforcement officers of any Indian tribe that has contracted or compacted any or all federal law enforcement functions through a contract or compact entered into pursuant to the Indian Self-Determination and Education Assistance Act to enforce federal law within the tribe's jurisdiction if those officers meet certain qualifications. These qualifications include completing training and passing an adjudicated background investigation. Further, the bill deems a tribal law enforcement officer who is acting under an authorized contract or compact as a federal law enforcement officer for the purposes of certain federal laws, including for injury and death, retirement, and pension benefits. The Department of the Interior must (1) develop procedures for credentialing tribal officers to confirm these officers meet minimum certification standards and training requirements for Indian country peace officers, and (2) issue guidance to implement this bill. The bill also requires the Department of Justice to coordinate and provide oversight for its functions and programs to ensure a coordinated approach for public safety in Indian communities.