Sample selection model is a solution to eliminate the nonresponse bias. In some applications nonresponse is a multilevel variable with respect to its reasons of occurring. In these cases, the sample selection model can be extended such that a model to be considered for each of the nonresponse reasons. Also, in many cases, the reasons for nonresponse have priority over each other. In other words, it is not possible to observe all of the nonresponse reasons simultaneously. For example, in a survey with two noncontact and refusal reasons, noncontact has priority over refusal and refusal can be observed if the contact to the respondent can be established. For analyzing such extended model, a Bayesian inference approach with multiple selection rules using multivariate normal, inverse gamma and LKJ distributions as prior distributions for parameters and possibility of priority for nonresponse reasons is presented. Simulation studies are performed and an establishment survey data set is analyzed to demonstrate the performance of the proposed method. For sensitivity analysis of nonresponse on the parameters of interest, posterior displacement is applied.