I have received a refund for my car insurance premiums more than once, and have never had to request it in writing.
I always pay my insurance in one lump annual sum, so if I have any changes to my policy, I have a refund coming.
Once I sold an old car I had and did not replace it with another car for quite awhile. I received a refund on my premium because I had paid for the entire year up front.
Since I no longer needed the insurance when I sold the car, they sent me a refund check.