Recent studies in flies and rodents have shown that animals switch between a small number of ‘behavioral states’ during decision-making. However, the majority of studies infer these state switches only from behavioral measurements such as choices or movements. To provide greater insight into the internal processes that guide these switches, we developed a method for identifying state changes from behavioral measurements and neural responses. We applied this method to an evidence accumulation task studied in rats. Our method models trial-to-trial state switches with a hidden Markov model (HMM) and within-trial latent dynamics with a drift-diffusion model (DDM). The resulting model provides a ‘DDM-HMM’ account of state-dependent neural activity and behavior. We applied this model to neural recordings in two brain regions, anterodorsal striatum and posterior parietal cortex, and found strong support for the hypothesis that neural responses switch states on a trial-to-trial basis and that these switches are informative about behavior. Parameters of the fitted model indicated that the accumulation dynamics underlying neural activity differed strongly between two different states. The model identified a low-noise ‘early-weighting’ state, where early stimuli were weighted more strongly than late stimuli, and a high-noise ‘leaky’ state, where stimulus information decayed during each trial. On trials in the low-noise state, neurons more strongly reflected accumulated evidence and task performance was better. Moreover, choice could be decoded accurately from neural activity in this state, while neural activity in high-noise state trials carried virtually no choice information. These findings suggest that rodents switch between behavioral strategies during decision-making, that a signature of these switches can be identified in neural responses, and that switches correspond to changes in specific cognitive ‘strategies’ for this task. Previous analyses of decision-making dynamics in well-trained animals have largely assumed a stationary brain state, an assumption that our results strongly call into question.