No Money Bail Act This bill restricts the use of money bail (i.e., the payment of money as a condition of pretrial release) in criminal cases. Specifically, it prohibits the use of money bail in federal criminal cases. Additionally, it amends the Omnibus Crime Control and Safe Streets Act of 1968: to make a state that uses a money bail system ineligible for funds under the Edward Byrne Memorial Justice Assistance Grant Program; and to establish grants: (1) for developing alternative bail systems in state and local court systems; and (2) for implementing the National Pretrial Reporting Program to collect data on how state and local courts process defendants. The Government Accountability Office must assess the alternative bail systems used by states.