According to the Ohio Department of Insurance when you buy liability insurance, your insurance agent or company may offer you Uninsured and Underinsured Motorist (UM/UIM) bodily injury coverage. This coverage takes the place of the liability coverage the other driver did not have and pays for injuries to you and your passengers when the other driver did not have enough insurance to pay for your injuries.
If you purchase this coverage, you cannot buy more coverage for UM/UIM BI than you have for liability coverage. Ohio law does not allow you to protect yourself better than you protect others.
Uninsured motorist property damage (UMPD) is a separate type of UM coverage that pays for physical damages to property caused by an uninsured driver. However, since collision and UMPD pay for the same damages, you do not need UMPD if you have collision coverage.
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Normally if you are involved in an accident with an unidentifiable driver, you must show that his or her negligence caused the accident and your resulting injuries and property damage. The OH DOI does not mention if UMPD will cover a hit and run accident or not so if you already have this coverage read your policy and/or ask your agent.
Typically, this should be covered under Comprehensive and/or Comprehensive/Other Than Collision coverage and not UMPD.
If you are thinking of purchasing UMPD coverage for your vehicle in Ohio, check with the insurance company you are going through to find out if damage from a hit and run would be covered with this or if you would be better off with collision coverage instead. | 
