This paper develops semiparametric Bayesian methods for inference of dynamic Tobit panel data models. Our approach requires that the conditional mean dependence of the unobserved heterogeneity on the initial conditions and the strictly exogenous variables be specified. Important quantities of economic interest such as the average partial effect and average transition probabilities can be readily obtained as a by-product of the Markov chain Monte Carlo run. We apply our method to study female labor supply using a panel data set from the National Longitudinal Survey of Youth 1979.