Supporting Family Mental Health in CAPTA Act This bill revises various programs that address the prevention and treatment of child abuse. For example, the bill expands the Child Welfare Information Gateway to include best practices for referrals to resources for physical, behavioral, and mental health and developmental needs. The bill also revises child abuse research programs to include elements such as (1) effective methods to address geographic, racial, and cultural inequities in the child welfare system; and (2) prevention of child abuse and neglect in families that have not had contact with the child welfare system. It further specifies that certain technical assistance must address, as applicable, best practices to prevent child abuse and neglect in families with complex needs (i.e., those who have experienced domestic violence or substance use disorders). Additionally, the bill makes changes to specified grant programs for child abuse and neglect. Among these changes, it requires programs to include training on (1) improving coordination among child protective services agencies, health care providers, and community resources; and (2) the links between child abuse and neglect and domestic violence and approaches to working with families with mental health needs or substance use disorders. It also modifies the contents of applications related to these grants.