If you would like to authorize someone to use your car, here is a sample template you can use to write a car authorization letter.
Subject: Car Authorization Letter
I, (Name), resident of (Address), own a (Car name and details) with the registration number (Number). Due to unforeseen circumstances, I am unable to drive my car. In my absence, I would like to authorize (Authorized Name) with a registration ID (Number) to take hold of my vehicle.
I request you to please update the required information in your system for future references.