Center to Advance, Monitor, and Preserve University Security Safety Act of 2013 or the CAMPUS Safety Act of 2013 - Amends the Omnibus Crime Control and Safe Streets Act of 1968 to authorize the Attorney General to establish and operate a National Center for Campus Public Safety.

Tasks the Center with strengthening the safety and security of institutions of higher education (IHEs) by: (1) training IHE public safety personnel and their collaborative partners; (2) fostering relevant research; (3) collecting and disseminating information and best practices regarding campus safety; (4) developing protocols and best practices to prevent, protect against, and respond to dangerous and violent situations that threaten the campus community; and (5) promoting cooperation among public safety and emergency management personnel of IHEs and their collaborative partners, including law enforcement, emergency management, and mental health agencies.

Allows states and localities to use Edward Byrne Memorial Justice Assistance Grants to make subawards to IHEs and other nonprofit organizations to assist the Center in carrying out those functions.