Strengthening Medicaid for Serious Mental Illness Act This bill allows state Medicaid programs to cover intensive community-based services for adults with serious mental illnesses. Specifically, states may provide for coverage of services that include (1) treatment services that are available 24/7, involve multidisciplinary care teams, and that are designed to improve outcomes for adults with mental illnesses who are at high risk of homelessness, psychiatric crisis, or hospitalization or who are involved in the criminal justice system (i.e., assertive community treatment); (2) employment support; (3) peer support; (4) community-based mobile crisis intervention services; (5) intensive case management; and (6) housing support. The bill provides funds for state planning grants with respect to such coverage. It also provides for an enhanced federal matching rate, also known as the Federal Medical Assistance Percentage (FMAP), for such services.