Renters Insurance is meant to cover your personal belongings inside your rental unit or extended to storage units, inside your car, etc. It is not meant to cover any portion of the rental unit, house , condo, etc that you are renting. The owner is responsible for the shell or actual real property.
If you are negligent and damaged the garage doors with your vehicle then your auto insurance would normally cover the damage under your "Property Damage" portion of the auto policy.
Business Development Officer, T.D. McNeil Insurance Services, Fresno, California
A garage door would be covered under the dwelling part of the fire policy carried by the landlord. However, if the damage was caused by your negligence and the landlord threatens to sue you, report the threat to the insurance company. There could be coverage under the liability section of your renter’s policy.
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If you are negligent and damaged the garage doors with your vehicle then your auto insurance would normally cover the damage under your "Property Damage" portion of the auto policy.