Free Consults: (614) 500-3836. While Ohio does not currently have a red flag law, there are other laws restricting who can own guns in the state and what guns people can buy.Weapons possession is regulated in Ohio, and only certain authorized individuals are allowed to possess dangerous ordnances. While Ohio does not currently have a red flag law, there are other laws restricting who can own guns in the state and what guns people can buy. How Firearms Background Checks Work. Unlawful weapons possession cases are notoriously complex. Firearms are not prohibited on the premises. Transporting in Motor Vehicles. Ohio state law lays out categories of persons who are prohibited from purchasing or possessing firearms. Prohibit anyone convicted of a felony and anyone subject to a domestic violence protective order from possessing a firearm.