Preventing and Addressing Trauma with Health Services Act or the PATHS Act This bill establishes grants to increase access to trauma support and mental health care for individuals who have experienced gun violence in communities with higher rates of violence-related deaths than the national average. The Substance Abuse and Mental Health Services Administration (SAMHSA) must award the grants to nonprofit or community organizations, government agencies, or health care institutions that offer mental health services. In awarding these grants, SAMHSA may give preference to community health centers, federally qualified health centers, and applicants proposing to work in partnership with other eligible entities.