The crossbar assembly includes a crossbar spanned between two side rails spaced apart from each other and sliding means fixed to both ends of the crossbar for slideably engaging the crossbar with the side rails. The sliding means including a rotatable lever, a lower clamp operative in conjunction with the rotatable lever, and a pad on which the side rail sits. The side rails disposed at the left side and right side of the roof panel of a vehicle have different bottom surfaces. Moreover, the pads of the sliding means, which directly contact the bottom surfaces of the side rails, have different sitting surfaces in order to tightly contact with the side rails. Accordingly, it is possible to effectively prevent the crossbar from being installed to the side rails in a reverse direction.