A bracket device includes a bracket, a fastening member, a supporting frame, and a fitting. The fastening member is movable with respect to the bracket. Once the supporting frame is operated and thus displaced with respect to the bracket to a first position, the fastening member is supported by the supporting frame and hence in a particular position. Once the supporting frame is operated and thus displaced with respect to the bracket to a second position, the fastening member is not supported by the supporting frame and therefore no longer in the particular position. When the fitting is at a predetermined position, the supporting frame is prevented from displacement from the first position to the second position.