In order to increase mental health equity among the most vulnerable and marginalized communities, it is important to increase access to high-quality therapists. One facet of address these needs, is to provide timely feedback to clinicians as they interact with their clients, in a way that is also contextualized to specific clients and interactions they have had. Dynamical systems provide a framework through which to analyze interactions. The present work applies these methods to the domain of automated psychotherapist evaluation for Cognitive Behavioral Therapy (CBT). Our methods extract local dynamic modes from short windows of conversation and learns to correlate the observed dynamics to CBT competence. The results demonstrate the value of this paradigm and outlines the way in which these methods can be used to study and improve therapeutic strategies.