According to the taxiing pilot, during taxi to the run-up area in order to perform a maintenance check, he attempted to maneuver around an airplane that had stopped in the non-movement area. He reported that the left wing of his airplane impacted the tail of the stopped airplane. According to the pilot of the stopped airplane, he had taxied out of the refuel station in order to allow other aircraft to refuel. He reported that he taxied south and stopped in the non-movement area next to the aircraft tie downs, where he remained stopped for approximately five minutes as he set up the radios and received the ATIS information for his flight. He reported that he felt an impact from the rear of his airplane; he shut down his engine, and exited the airplane. The taxiing airplane sustained minor damage to the left wing and stopped airplane sustained substantial damage to the aft fuselage and vertical stabilizer. Both pilots reported that there were no mechanical failures or anomalies with the airplane prior to or during the taxi that would have prevented normal flight operation.