According to a company report, after boarding all other passengers, gate agents proceeded with boarding a quadriplegic passenger who required assistance and use of an aisle chair to be moved to his seat on the airplane. A seatbelt and additional belts across the passenger's chest were used to secure him in the aisle chair while moving him onboard. When the belts were removed in order to transfer the passenger from the aisle chair to the airplane seat the passenger slid to the floor. The passenger was then lifted into his seat by the gate agents. According to crew statements, after the gate agents left the airplane and the jetway had been retracted, a flight attendant (FA) observed that the passenger appeared to be injured and the crew requested emergency services. The passenger was transported to a hospital and diagnosed with a broken right tibia.