Helping Emergency Responders Overcome Act or the HERO Act This bill establishes and authorizes behavioral health programs for law enforcement officers, firefighters, emergency medical services personnel, 9-1-1 operators, and other public safety officers. Specifically, the Fire Administration within the Federal Emergency Management Agency must develop resources for educating mental health care providers about treating firefighters and emergency medical services personnel. In addition, the Department of Health and Human Services (HHS) must develop best practices and resources for identifying, preventing, and treating post-traumatic stress disorder and co-occurring disorders in public safety officers. HHS must work with relevant federal departments to incorporate these resources into federal training programs for public safety officers. The bill also authorizes HHS to set up a public safety officer suicide-reporting system and a grant program for peer-support behavioral health and wellness programs within fire departments and emergency medical services agencies.