Yes, your car being keyed would normally be found to be vandalism and thus covered under your Comprehensive coverage. However unless your insurance company waives your Comprehensive deductible you still would have to pay it.
Vandalism to your vehicle, such as a door being keyed, should be reported to the police and your insurance company. If the insurance company finds that the damages to your car are from an act of vandalism then it should be covered under your Comprehensive coverage with the related deductible being due. Physical damage coverage, such as Comprehensive, comes with a deductible amount that you chose when you set up your policy.
A deductible is due normally for your Collision or Comprehensive coverage whether you were at-fault in the accident or incident or not. To get your door that was keyed fixed report the act of vandalism to the police and get a report and also contact your car insurance agent to make a Comprehensive claim.
If your agent is not able to explain to you what to do in this situation or fulfill your car insurance needs, contact a CarInsurance.com agent and they can explain not only insurance terms and explain claim procedures but also tell you how they can get you the best rates.