Continuous-state POMDPs provide a natural representation for a variety of tasks, including many in robotics. However, existing continuous-state POMDP approaches are limited by their reliance on a single linear model to represent the world dynamics. We introduce a new switching-state (hybrid) dynamics model that can represent multi-modal state-dependent dynamics. We present a new point-based POMDP planning algorithm for solving continuous-state, discrete-observation POMDPs using this dynamics model and approximate the value function as a mixture of a bounded number of Gaussians. We compare our hybrid dynamics model approach to a linear dynamics continuous-state planner and a discrete-state POMDP planner and show that in some scenarios we can outperform such techniques.