Suicide Prevention Research INnovaTion Act or the SPRINT Act - Amends the Public Health Service Act to require the Director of the National Institute of Mental Health to use funds made available by this Act exclusively for the purpose of conducting and supporting: (1) research on the determinants of self-directed and other violence associated with mental illness, including studies designed to reduce the risk of self-harm, suicide, and interpersonal violence, especially in rural communities with a shortage of mental health services; and (2) brain research through the Brain Research Through Advancing Innovative Neurotechnologies (BRAIN) Initiative.