After being newly painted at Prospectville, PA, the plane was being flown to Farmingdale, NY where the pilot received a special VFR clearance. According to the pilot, the gear was lowered on the downwind leg for runway 19, but an abnormal noise was heard and no safe indication was observed. He stated that after cycling the gear, normal indications were received on both, the lights and the mechanical indicators. After turning to final approach, a 360 degree turn was made to lose altitude, then the landing was continued. A witness observed the aircraft on final and during landing with the gear retracted. Investigators found the landing gear handle in the down position, the mechanical indicator in the up position, and the landing gear relay circuit breaker out. When the battery was first turned on to check the system, an odor from an electrical component was noted and the relay breaker was pulled. However, after that, both the emergency and normal gear systems were checked, no discrepancies were found.