I'm in Ohio. I've never been in a Job and Family services building. I have had spenddown Medicaid for years (in conjunction with Medicare). I do the paperwork online or mail it in. It's never been a problem. You are allowed to have some property. A car, a home. I have never had trouble with having some money in savings. Not a lot but a little. Other possessions they don't ask about.

https://benefits.ohio.gov/