ONCE THE SINGLE ENGINE, RETRACTABLE GEAR AIRPLANE HAD TAKEN OFF THE PILOT ENGAGED THE OVERRIDE FUNCTION OF LANDING GEAR'S AUTO EXTENSION SYSTEM. PRIOR TO HIS ARRIVAL AT THE DESTINATION THE PILOT DISENGAGED THE OVERRIDE FUNCTION. THE PILOT PERFORMED HIS PRELANDING CHECKLIST DURING HIS APPROACH TO LAND AND NOTED THREE GREEN LIGHTS INDICATING GEAR EXTENSION. UPON DEPARTURE THE PILOT ACCELERATED TO A HIGHER THAN NORMAL SPEED, DUE TO PERCEIVED RESIDUAL WAKE TURBULENCE, THE AIRPLANE LIFTED OFF AND THE LANDING GEAR BEGAN TO RETRACT. THE AIRPLANE SETTLED ONTO THE RUNWAY AND SLID OFF INTO THE GRASS. THE GEAR SELECTOR SWITCH WAS FOUND IN THE UP POSITION. THE LANDING GEAR AUTO EXTENSION SYSTEM FUNCTIONS ON THE BASIS OF LOWER AIRSPEEDS AND REDUCED POWER. THE PILOT COULD NOT RECALL IF HE HAD PUT THE GEAR SELECTOR SWITCH IN THE DOWN POSITION DURING HIS ARRIVAL AT THE ACCIDENT AIRPORT.