Rear ended someone in a club car wash

I have a membership for an automatic carwash (club car wash) where your car goes through automatically. While I was following instructions to move forward, my car, already in neutral and in the wash process, rear-ended the vehicle in front. We both suspect a car wash malfunction. Despite the car wash's unhelpfulness, they requested my VIN number, which I hesitated to provide out of fear that it might impact my insurance. Seeking advice on whether sharing the VIN would involve my insurance or how to handle this situation without affecting my rates