Who would be paying the towing truck company's fee.the expensies of not having my only car?

I was pulled over by officers in 2/3/15, dropped me off my car and my car was towed away and impounded. Officer said: The reason that you don't have insurance for the period July 14 to Nov 30/ 2013. I knew that I had insurance and I called the insurance company and confirmed that I had insurance during that period. Next day 2/4 I called the MVA and told me the Insurance FR19 form July 14 to Nov. 30/2013 which states that I have insurance wasn't sent to MVA. What was sent cancellation and I figured out why from the insurance company ?! because I did change the payment date but the insurance restated my insurance at that time and cancelled the previous one. But the insurance was continuous/no laps. Note that I changed my address but never changed in the car title. which I am responsible for it. I thought MVA might sent a notice in the old add. and I didn't get. Now I want my car back who is responsible to pay the towing truck?, insurance or the MVA. any other Inconveniences' expenses