Someone recently found my blog searching for "Does Ohio Medicaid Pay for a Service Dog?" It doesn't. Neither does Medicaid in any other state. Neither does Medicare. I don't think the VA does, but they might under certain limited circumstances. No regular insurance companies do, not Blue Cross Blue Shield, not Anthem, not Cigna, not Aetna, etc.
Currently, if you want a service dog, you have to pay for it yourself. You can ask for donations. I got help from some local churches to pay for my service dog. But insurance won't cover it, and Medicare won't cover it, and Medicaid won't cover it. I think they should, or should at least help with the cost, but they don't at this time.