The present paper considers the testing of unit root hypothesis for an autoregressive model in the presence of a stationary covariate using Bayesian framework. The posterior odds ratio for the unit root hypothesis has been derived under appropriate prior assumptions for the parameters of the model. The results of a numerical simulation are presented to elaborate the theoretical findings and observe the impact of ignoring covariate in posterior odds ratio. An numerical illustration is also carried out on Nelson and Plosser (1982) data and get similar results.