Human interaction involves the organization of a collection of sensorimotor systems across space and time. The study of how coordination develops in child-parent interaction has primarily focused on understanding the development of specific coordination patterns from individual modalities. However, less work has taken a systems view and investigated the development of coordination among multiple interdependent behaviors. In the present work, we used Granger causality as a mathematical model to construct dyadic causal networks of multimodal data collected from a longitudinal study of child-parent interaction. At a group-level, we observed increases in the number of causal links and in the strength of such links in dyadic interaction from 9-months to 12-months. At an individual-level, we observed high variability in the types of causal links that emerged across developmental ages. We discuss these results in terms of a multicausality hypothesis for the development of human coordination.