Safer Communities Act of 2019 This bill establishes grants for mental health programs, revises certain prohibitions related to firearms, and revises criminal history reporting systems. Specifically, it provides grants to expand mental health crisis assistance programs, support comprehensive school mental health programs, and enhance mental health and substance abuse needs of prisoners. The Department of Health and Human Services must expand research on violence associated with mental illness and substance abuse disorders. The Centers for Disease Control and Prevention must expand the National Violent Death Reporting System to all 50 states and research the causes, mechanisms, prevention, diagnosis, and treatment of injuries from gun violence. Additionally, physicians are not prohibited from asking patients about guns in their homes, speaking to a patient about gun safety, or reporting a patient's threat of violence. The bill authorizes state grants to remove firearms from individuals who pose a threat to themselves or others. The Department of Justice must promptly notify law enforcement agencies when a prohibited person attempts to purchase a firearm. It also revises the National Instant Criminal Background Check System to establish procedures to restore firearm ownership rights after a mental health adjudication or commitment, authorize state grants for the automation and transmittal of mental health and criminal history records, and require certain annual reports and quarterly updates. Finally, it reauthorizes through FY2024 the National Criminal History Records Improvement Program.