Suicide Prevention Research INnovaTion Act or the SPRINT Act - Amends the Public Health Service Act to direct 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 in 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.