Effective Suicide Screening and Assessment in the Emergency Department Act of 2019 This bill establishes a competitive grant program for up to 40 hospitals with emergency departments and certain on-site professionals to help connect patients in emergency departments who are at risk of suicide with treatment and mental health services. Grants may be used to train emergency department providers and establish certain policies and procedures related to the identification, assessment, and treatment of, and care coordination for, individuals who are at risk of suicide. In awarding the grants, the Department of Health and Human Services may give preference to specified types of hospitals, such as critical access hospitals and hospitals in areas with suicide rates higher than the national average.