Active Shooter Alert Act of 2022 This bill requires a designated officer of the Department of Justice to act as the national coordinator of an Active Shooter Alert Communications Network regarding an emergency involving an active shooter. The bill sets forth duties of the coordinator, including to work with state, tribal, and local governments to encourage coordination of various elements of the network. The coordinator must also encourage federal, state, local, and tribal government agencies to establish procedures for responding to active shooters. Finally, the bill requires the Government Accountability Office to study and report on state and local responses to active shooters and situations requiring the issuance of a public alert or warning.