If "taken without permission" means the vehicle was stolen, your insurance should pay for damages that it would normally cover and then seek reimbursement from the person who stole the car. If the car was taken by a friend or excluded driver, you must bear the burden of proving that you did not give permission, and the insurance company will deny the claim until you do so. Insurance coverage for your situation is not as cut-and-dried as you may think, involving several important factors.
Type of Claim
Liability car insurance protects the named drivers on your policy. If someone who was not listed on the policy causes the accident, the insurance company can deny liability because they do not have that person calculated into the risk of insuring the vehicle. On the other hand, collision insurance is intended to pay for damages to your car, and will pay for them even if the car was taken without your permission. You will be responsible for proving that you did not give permission to drive the car, and any deductibles on the coverage will need to be satisfied first. Finally, comprehensive car insurance is used to pay for damages to the vehicle if it was stolen, and will require a copy of the police report when the theft was first recorded.
Excluded drivers are people in your home that are expressly forbidden from driving your car. If an excluded person drives the car and gets in an accident, your only recourse is to prove that the person took the vehicle without permission. To do that, you will generally have to file a stolen vehicle report with the police, and the excluded driver would then be prosecuted as allowed by law, including being held responsible for the damages they caused.
Non-Permission Vs. Theft
The main problem is that non-permission and theft are not the same thing. Where theft is concerned, comprehensive car insurance will pay for any damages, but a person driving your car without permission becomes your own responsibility because you are the owner of the vehicle and should have control of who will be driving it at all times. The insurance company has the right to deny the claim unless you provide them with a copy of a police report for a stolen vehicle.
Burden of Proof
Proof that you did not give permission to drive the car for someone living in your household is difficult. You will have to present evidence that you had taken all reasonable precautions to prevent that person from driving, and that the guilty driver circumvented your efforts. To avoid this situation, most insurance companies will require you to give them notification of anyone who will be using the vehicle, and the insurer reserves the right to deny coverage even then.