The company has a right to decide what items it will allow onto its property. It may ask you to voluntarily allow your bags and whatnot to be searched. You have a right to refuse to let them search your private belongings. They have a right to fire you and ban you from their property if you refuse.
I’m not an Ohio lawyer, but this sounds right, assuming that the employee is (like most) an employee at will. The answer might change if there’s a contract (union or otherwise) governing the employment relationship, but that would depend on the contract.