Previous studies suggest that bimanual coordination recruits neural mechanisms that explicitly couple control of the arms, resulting in symmetric kinematics. However, the higher symmetry for actions that require congruous joint motions compared with noncongruous joint motions calls into question the concept of control coupling as a general policy. An alternative view proposes that codependence might emerge from an optimal feedback controller that minimizes control effort and costs in task performance. Support for this view comes from studies comparing conditions in which both hands move a shared or independent virtual objects. Because these studies have mainly focused on congruous bimanual movements, it remains unclear if kinematic symmetry emerges from such control policies. We now examine movements with congruous or noncongruous joint motions (inertially symmetric or asymmetric, respectively) under shared or independent cursors conditions. We reasoned that if a control policy minimizes kinematic differences between limbs, spatiotemporal symmetry should remain relatively unaffected by inertial asymmetries. As shared tasks reportedly elicit greater interlimb codependence, these conditions should elicit higher bilateral covariance regardless of inertial asymmetries. Our results indicate a robust spatiotemporal symmetry only under inertially symmetric conditions, regardless of cursor condition. We simulated bimanual reaching using an optimal feedback controller with and without explicit costs of kinematic asymmetry, finding that only the latter mirrored our empirical data. Our findings support the hypothesis that bimanual control policies do not include kinematic asymmetry as a cost when it is not demanded by task constraints suggesting that kinematic symmetry depends critically on mechanical movement conditions.NEW & NOTEWORTHY Previously, the control coupling hypothesis and task-dependent control hypothesis have been shown to be robust in the bimanually symmetrical movement, but whether the same policy remains robust in the bimanually asymmetrical movement remains unclear. Here, with evidence from empirical and simulation data, we show that a spatiotemporal symmetry between the arms is not predicated on control coupling, but instead it is predicated on the symmetry of mechanical conditions (e.g. limb inertia) between the arms.