In complex environments, animals can adopt diverse strategies to find rewards. How distinct strategies differentially engage brain circuits is not well understood. Here we investigate this question, focusing on the cortical Vip-Sst disinhibitory circuit. We characterize the behavioral strategies used by mice during a visual change detection task. Using a dynamic logistic regression model we find individual mice use mixtures of a visual comparison strategy and a statistical timing strategy. Separately, mice also have periods of task engagement and disengagement. Two-photon calcium imaging shows large strategy dependent differences in neural activity in excitatory, Sst inhibitory, and Vip inhibitory cells in response to both image changes and image omissions. In contrast, task engagement has limited effects on neural population activity. We find the diversity of neural correlates of strategy can be understood parsimoniously as increased activation of the Vip-Sst disinhibitory circuit during the visual comparison strategy which facilitates task appropriate responses.