Medicaid.gov doesn't have a state office locator. All state-related info doesn't appear to be aimed at citizens/customers... why is this? There is no comprehensive list you can access of all state Medicaid offices on any other .gov site, either. Benefits.gov provides a place where you can find contact info for these offices, by state (http://www.benefits.gov/benefits/browse-by-category/category/MED)... but Ohio and South Carolina are missing from this list!
Bottom line, though, is that medicaid.gov should be the repository of this information.