The pilot reported that during the approach to land he remembered lowering the landing gear and hearing a change in the "wind noise." He thought he had a green light indication; however, he stated that the way the sun was it could have been a reflection. A witness and his wife who were driving near the airport saw the airplane on short final without the landing gear extended. They both watched as the airplane landed on the runway without extending the landing gear. The airplane slid about 500 feet down the runway. The police officer who responded to the accident observed two sets of propeller striations on the runway. The officer documented the marks with digital photographs. The FAA examined the airplane after the accident at a local FBO. During the examination the FAA was able to extend the landing gear by use of the landing gear selector switch. The main landing gear operated normally; the nose gear did not extend due to a broken connecting rod. The FAA inspector reported that the broken connecting rod was as a result of the accident sequence.