In order to solve complex, long-horizon tasks, intelligent robots need to carry out high-level, abstract planning and reasoning in conjunction with motion planning. However, abstract models are typically lossy and plans or policies computed using them can be unexecutable. These problems are exacerbated in stochastic situations where the robot needs to reason about, and plan for multiple contingencies. We present a new approach for integrated task and motion planning in stochastic settings. In contrast to prior work in this direction, we show that our approach can effectively compute integrated task and motion policies whose branching structures encoding agent behaviors handling multiple execution-time contingencies. We prove that our algorithm is probabilistically complete and can compute feasible solution policies in an anytime fashion so that the probability of encountering an unresolved contingency decreases over time. Empirical results on a set of challenging problems show the utility and scope of our methods.