Your letter should include a concise factual summary of the accident, an overview of your damages, your settlement demand, and not much more. If you are injured in a motor vehicle accident, file a written notice of claim with the No-Fault insurer that identify the injured person(s).Learn about cash settlements in your case and how they are accepted and approved. David Azizi explains the process of cash settlement acceptance. A demand letter serves as a formal request to the insurance company, outlining the incident, the injuries sustained, and the financial losses incurred. A car accident settlement letter is a formal written communication aimed at resolving a dispute amicably before proceeding to litigation. Below is an example of a car insurance demand letter. Make sure to tailor it to your own accident and situation. Car Accident Private Settlement Letter – What to Know. The private settlement letter follows an agreement between individuals who have been in a car accident.