We have studied the steady-state properties of a hybrid optomechanical system, where a Y-type four-level atomic ensemble is confined in a microcavity with an oscillating mirror in one end. We find that the hybrid system will have multistability for the oscillating mirror and the confined atoms as the elastic coefficient of the spring decreases. When the elastic coefficient is very large, the oscillating mirror hardly affects the optomechanical system, therefore the system and the atomic ensemble have a single steady-state solution. However, when the elastic coefficient is small enough, the multiequilibrium positions of the oscillating mirror will be found, and the steady-state behaviors of the atomic ensemble confined in the microcavity may be affected. As a result, the susceptibility of the atomic ensemble will have multiple steady-state solutions and the probe absorption and dispersion will be changed as well. It has also been found that the number of steady-state solutions of the entire system could be controlled by changing the value of the elastic coefficient. These results may have potential applications in the area of high-precision quantum measurement and quantum information processing.