Can a repo company charge you a fee for your personal belongings in Ohio?

Yes, not only may they, they likely will. When personal property is found in a repossessed vehicle, provided it is not illegal substances or firearms, the repossessing company must take an inventory of all property. They are required to store it pursuant to the individual laws of every state, Ohio is no exception, and they may charge staroage fee for that property. It is unlikely that they will release it to you until that amount is paid, and they may not release to anyone but the registered owner of the vehicle.