Suicide Prevention Act This bill requires the Department of Health and Human Services (HHS) to establish two grant programs to prevent self-harm and suicide. First, HHS must award grants to state, local, and tribal health departments to expand surveillance of self-harm. In awarding these grants, HHS must prioritize recipients in areas that experience rates of nonfatal suicidal behavior that are above the national average and must take into account other factors such as the unique needs of rural communities. As a condition of receiving this funding, recipients must agree to share data on suicide and self-harm with the Centers for Disease Control and Prevention. Second, HHS must award grants to hospital emergency departments for programs to prevent suicide attempts among patients after discharge, including programs for screening patients for self-harm and suicide and providing short-term preventive services, as appropriate. In addition, HHS must develop standards of practice for such screenings.