Understanding how multiple brain regions interact to produce behavior is a major challenge in systems neuroscience. Sensory-driven decision making, in particular, has been shown to involve context-dependent processing in multiple brain regions, but a precise description of the interactions between regions remains an open problem. Addressing this problem requires new methods for inferring multi-region activity that account for sensory inputs and communication between brain regions. Here we develop multi-region switching state space models with higher-order autoregressive dynamics, allowing for time-varying estimation of directed, multi-region interactions. The approach models high dimensional multi-region observations as emissions from coupled, low dimensional dynamical systems with explicit local dynamics and communication across time-lags. To fit the model, we derive variational Laplace EM (vLEM) for autoregressive dynamical systems, extending vLEM to the case of higher order AR dynamics. We additionally introduce a measure of the volume of communications between brain regions across time in the model, allowing us to quantify the directional ’messages’ communicated between regions at each timepoint. We use the model to analyze two calcium imaging datasets in mice performing a sensory decision making task: mesoscale wide-field recordings, and cellular-resolution two-photon mesoscope recordings, simultaneously from 16 and 3 brain regions, respectively. In both cases, our method reveals multiple distinct, task-driven dynamical states, and produces rich estimates of communication flows across regions, revealing interactions that match known connectivity and hypothesized functional roles of different areas. Preliminary analysis suggests large-scale cortico-cortical interactions are a more important determinant of cortical dynamics than the sensory input, despite the sensory nature of the task. Thus, we introduce an important approach to analyzing and understanding multiregion neural activity and communication in decision making tasks.