This paper presents a study of the dynamic coupling between a user and a virtual character during body interaction. Coupling is directly linked with other dimensions, such as co-presence, engagement, and believability, and was measured in an experiment that allowed users to describe their subjective feelings about those dimensions of interest. The experiment was based on a theatrical game involving the imitation of slow upper-body movements and the proposal of new movements by the user and virtual agent. The agent's behaviour varied in autonomy: the agent could limit itself to imitating the user's movements only, initiate new movements, or combine both behaviours. After the game, each participant completed a questionnaire regarding their engagement in the interaction, their subjective feeling about the co-presence of the agent, etc. Based on four main dimensions of interest, we tested several hypotheses against our experimental results, which are discussed here.