Veterans Census-Enabled National Treatment Equitable Resource Supplement for Mental Health Act of 2023 or the Vet CENTERS for Mental Health Act of 2023 This bill requires the Department of Veterans Affairs (VA) to ensure that there is a minimum number of Vet Centers located in each state. Vet Centers are community-based counseling centers that provide social and psychological services to eligible veterans, service members, and their families. The minimum number of Vet Centers required in each state is generally based on the state's geographic size or the number of veterans located in the state. The VA must establish additional Vet Centers as necessary to meet the minimum required number for each state. The VA may establish the additional Vet Centers at facilities made available by a state, local government, or recognized Indian tribe. If a state needs more than one additional Vet Center to meet its minimum requirement, the VA must establish at least one additional Vet Center and may establish Vet Center outstations to cover the difference.