Mental Health First Aid Act of 2013 - Amends the Public Health Service Act to require the Secretary of Health and Human Services (HHS), acting through the Administrator of the Substance Abuse and Mental Health Services Administration (SAMHSA), to award grants to initiate and sustain mental health first aid training programs. Requires such a program to include: (1) core live training courses on the skills, resources, and knowledge necessary to assist individuals in crisis to connect with appropriate local mental health care services; (2) training on mental health resources, including the location of community mental health centers in the state and local community; and (3) training on action plans and protocols for referral to such resources.

States that the Secretary shall determine the categories of individuals to be trained.

Requires such programs to train individuals to accomplish: (1) safe de-escalation of crisis situations, (2) recognition of the signs and symptoms of mental illness, and (3) timely referral to mental health services in the early stages of developing mental disorders.

Requires the Secretary, in awarding grants, to: (1) ensure that grants are equitably distributed among the geographical regions of the United States, and (2) pay particular attention to the mental health training needs of populations and target audiences residing in rural areas.