Coronavirus Mental Health and Addiction Assistance Act of 2020 This bill provides emergency funds for the Substance Abuse and Mental Health Services Administration to award grants to establish a network of entities that provide mental health and substance use disorder programs during, or in connection with, the COVID-19 (i.e., coronavirus disease 2019) pandemic. Eligible entities include tribes, qualified nonprofit organizations, and partnerships of two or more eligible entities. Grant funds may be used for initiating or expanding telehealth services, support groups, and other activities to provide individuals with counseling and other resources to assist in the management of mental health or substance use disorders.