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The extent to which hand dominance may influence how each agent contributes to inter-personal coordination remains unknown. In the present study, right-handed human participants performed object balancing tasks either in dyadic conditions with each agent using one hand (left or right), or in bimanual conditions where each agent performed the task individually with both hands. We found that object load was shared between two hands more asymmetrically in dyadic than single-agent conditions. However, hand dominance did not influence how two hands shared the object load. In contrast, hand dominance was a major factor in modulating hand vertical movement speed. Furthermore, the magnitude of internal force produced by two hands against each other correlated with the synchrony between the two hands’ movement in dyads. This finding supports the important role of internal force in haptic communication. Importantly, both internal force and movement synchrony were affected by hand dominance of the paired participants. Overall, these results demonstrate, for the first time, that pairing of one dominant and one non-dominant hand may promote asymmetrical roles within a dyad during joint physical interactions. This appears to enable the agent using the dominant hand to actively maintain effective haptic communication and task performance.