How would an insurance claim affect your future rates in a hit and run accident that was not your fault?

According to my experience, it should not affect your insurance rates if you were not at fault. I was involved in a hit-and-run myself, and at the time I was too nervous to jot down the correct license plate. I filed the report anyways though.
Of course, due to the severity of the accident and whether or not you were injured, that would determine how much money your insurer need to shell out. However, as long as it's not your fault, they have no reason to increase your rates.

Good luck!