In this paper we consider the analysis of semiparametric models for binary panel data with state dependence. A hierarchical modeling approach is used for dealing with the initial conditions problem, for addressing heterogeneity, and for incorporating correlation between the covariates and the random effects. We consider a semiparametric model in which a Markov process prior is used to model an unknown regression function. Estimation is done by computationally efficient Markov chain Monte Carlo methods that exploit the underlying latent structure of binary data models, following Albert and Chib (1993). Simulation results suggest that the method performs well. In addition to estimation, we address the problem of model selection which is a key concern when dealing with a multitude of possible specifications. Moreover, we present a framework for calculating the average covariate effects, which deals with the nonlinearity and dynamic structure of the model. The techniques of this paper are applied to modeling of the intertemporal labor force participation decisions of a panel of 1545 married women. In this application, the data support a semiparametric model with multiple sources of heterogeneity and multi-lag state dependence.