Fish swimming together in schools interact via multiple sensory pathways, including vision, acoustics and hydrodynamics, to coordinate their movements. Disentangling the specific role of each sensory pathway is an open and important question. Here, we propose an information-theoretic approach to dissect interactions between swimming fish based on their movement and the flow velocity at selected measurement points in the environment. We test the approach in a controlled mechanical system constituted by an actively pitching airfoil and a compliant flag that simulates the behaviour of two fish swimming in line. The system consists of two distinct types of interactions – hydrodynamic and electromechanical. By using transfer entropy of the measured time series, we unveil a strong causal influence of the airfoil pitching on the flag undulation with an accurate estimate of the time delay between the two. By conditioning the computation on the flow-speed information, recorded by laser Doppler velocimetry, we discover a significant reduction in transfer entropy, correctly implying the presence of a hydrodynamic pathway of interaction. Similarly, the electromechanical pathway of interaction is identified accurately when present. The study supports the potential use of information-theoretic methods to decipher the existence of different pathways of interaction between schooling fish.