Alaska Tribal Public Safety Empowerment Act This bill expands the civil and criminal jurisdiction of certain Indian tribes over Alaska Natives and non-Alaska Natives in Alaska. Specifically, the bill recognizes and affirms that any Indian tribe in Alaska occupying an Alaska Native village may exercise (1) criminal and civil jurisdiction over Alaska Natives in the village; and (2) full civil jurisdiction over Alaska Natives and non-Alaska Natives in the village with respect to issuing and enforcing protection orders, excluding violators of protection orders from the village, and using other appropriate mechanisms to address matters in the village related to protection orders. The bill also directs the Department of Justice to establish a pilot program to provide certain Indian tribes with (1) general civil jurisdiction over Alaska Natives and non-Alaska Natives present in the Alaska Native village occupied by such tribe; and (2) criminal jurisdiction over Alaska Natives and non-Alaska Natives with respect to specific crimes, such as domestic violence, sexual violence, and stalking.