The crew chief is the head official in basketball who is responsible for making the final decision in a game. In college basketball, the crew chief or "senior official" is not allowed to overall the "umpires" or referees. The crew chief is the lead referee and acts as a captain for the group. Mainly, head coaches consult with the crew chief when they need an explanation of a call or have a complaint with a call.
The responsibilities of the crew chief are basically to have the final say on any call in a game. This is similar to the role of a coach to a coordinator as in both cases one answers to another. In this case, the other referees answer to the crew chief. Other than this they have the same responsibility as regular referees enforcing the game by calling things such as fouls or double dribbles.