One of the major challenges faced by explanations of imitation is the “correspondence problem”: how is an agent able to match its bodily expression to the observed bodily expression of another agent, especially when there is no possibility of external self-observation? Current theories only consider the possibility of an innate or acquired matching mechanism belonging to an isolated individual. In this paper we evaluate an alternative that situates the explanation of imitation in the inter-individual dynamics of the interaction process itself. We implemented a minimal model of two interacting agents based on a recent psychological study of imitative behavior during minimalist perceptual crossing. The agents cannot sense the configuration of their own body, and do not have access to other's body configuration, either. And yet surprisingly they are still capable of converging on matching bodily configurations. Analysis revealed that the agents solved this version of the correspondence problem in terms of collective properties of the interaction process. Contrary to the assumption that such properties merely serve as external input or scaffolding for individual mechanisms, it was found that the behavioral dynamics were distributed across the model as a whole.