Dam Safety Act of 2013 - Amends the National Dam Safety Program Act to authorize appropriations for the national dam safety program for FY2013-FY2016.
Requires the head of a federal agency, at the request of a state dam safety agency with respect to any dam the failure of which would affect the state, to provide information to that agency on the dam's condition and on its provisions for emergency operations.
Includes as a program objective to develop and implement a comprehensive dam safety hazard education and public awareness program to assist the public in mitigating against, preparing for, responding to, and recovering from dam incidents.
Permits the Administrator, in consultation with the National Dam Safety Review Board, to invite representatives from nongovernmental organizations to participate in Board meetings.
Prohibits the amount of funds allocated to a state to carry out the dam safety program from exceeding the amount committed by the state to implement program activities (currently, 50% of the reasonable cost of implementing the state dam safety program).