American Indian and Alaska Native Veterans Mental Health Act This bill directs the Department of Veterans Affairs (VA) to provide mental health and suicide prevention outreach to American Indian and Alaska Native veterans. Specifically, the bill requires that each VA medical center have a full-time minority veteran coordinator. The coordinator must receive training in the delivery of culturally appropriate mental health and suicide prevention services to American Indian and Alaska Native veterans. Further, the suicide prevention coordinator and minority veteran coordinator of each VA medical center must develop and disseminate a written plan for conducting mental health and suicide prevention outreach to all tribes and urban Indian health organizations within the area of the medical center.