Coordination of bilateral movements is essential for a large variety of animal behaviors. The olivocerebellar system is critical for the control of movement, but its role in bilateral coordination has yet to be elucidated. Here, we examined whether Purkinje cells encode and influence synchronicity of left-right whisker movements. We found that complex spike activity is correlated with a prominent left-right symmetry of spontaneous whisker movements within parts, but not all, of Crus1 and Crus2. Optogenetic stimulation of climbing fibers in the areas with high and low correlations resulted in symmetric and asymmetric whisker movements, respectively. Moreover, when simple spike frequency prior to the complex spike was higher, the complex spike-related symmetric whisker protractions were larger. This finding alludes to a role for rebound activity in the cerebellar nuclei, which indeed turned out to be enhanced during symmetric protractions. Tracer injections suggest that regions associated with symmetric whisker movements are anatomically connected to the contralateral cerebellar hemisphere. Together, these data point toward the existence of modules on both sides of the cerebellar cortex that can differentially promote or reduce the symmetry of left and right movements in a context-dependent fashion.