WITNESSES SAID THE PLT MADE 2 LOW PASSES OVER THE AIRSTRIP AFTER TKOF, THEN TURNED WEST & BGN A CLIMB. AFTER GLANCING ATTHE ACFT, A WITNESS HEARD THE ENG 'GET QUIET AS IF SHUT DOWN FOR A LANDING.' HE DIDN'T CONSIDER THIS UNUSUAL, SINCE ENGSWERE OFTEN THROTTLED BACK NR THE STRIP. LTR, THE ACFT WAS FND WHERE IT HAD CRASHED IN A STEEP NOSE DWN ATTITUDE ON A HDGOF SOUTH, APRX 1/2 MI WSW OF THE STRIP. ACFT DMG WAS TYPICAL OF A SLOW SPD IMPACT. NO EVIDENCE OF ENG PWR WAS EVIDENT &NO PREIMPACT PART FAILURE/MALFUNCTION WAS FND. THE ACFT WAS NOT REFUELED BEFORE FLT, BUT A WITNESS ESTD THERE WAS 5 GAL IN THE MAIN TANK & 7 GAL IN THE AUX TANK. BOTH TANKS WERE RUPTURED DRG IMPACT & AN ODOR OF FUEL WAS NOTED. THE ACFT WAS PLACARDED FOR AUTO FUEL AND AUTO FUEL WAS FOUND IN THE CARB.THE AUX FUEL VLV WAS FND IN THE 'OPEN' PSN, ALTHO IT WAS TO BE CLOSED EXCEPT TO DRAIN AUX FUEL TO THE MAIN TANK IN LVL FLT ONLY. TEMP & DEW POINT WERE 78 & 67 DEG, RESPECTIVELY. ICING PROBABILITY CHARTS SHOWED CARB ICING WAS POSSIBLE AT RATED PWR. THE CARB HEAT WAS FND IN THE COLD/OFF PSN.