If you're going to make an uninsured or underinsured motorist claim, you need to act fast. Drivers who get into a car accident without insurance in New York may face penalties, such as having to pay fines or facing driver's license suspension.If you are driving in NY and are involved in a crash you must file an MV-104 (Motorist report) if any of the following occurred. If her insurance accepts that she was fully at fault, they will pay for your damages, auto and medical, up to her policy limits. If the at-fault driver has no insurance coverage, the other driver can rely on underinsured or uninsured motorist coverage to cover accident-related damages. If the at-fault party in a car accident does not have car insurance, you have options. If you were involved in a car accident where you believe the other driver was at fault. Here is the form you must fill out. Your Liability Insurance: Since the accident is your fault, your liability insurance will come into play. After a car accident, the atfault driver's insurance company is responsible for paying for the other driver's related expenses.