1. The afferent input to the cerebellum is uncrossed. Proprioceptive information (from muscle spindles, Golgi tendon organs, joint and touch receptors) reaches the cerebellum mainly through the dorsal spinocerebellar tract. This tract enters via the inferior cerebellar peduncle and terminates in the vermis and intermediate zone on the same side as its origin - Guyton and Hall, p. 701-702. So each cerebellar hemisphere is informed about, and monitors, the movements of the limbs on its own side of the body.

2. The efferent output undergoes a double decussation. Output from the intermediate zone (via the interposed nucleus) and lateral zone (via the dentate nucleus) leaves through the superior cerebellar peduncle and crosses (1st decussation) to reach the contralateral red nucleus and ventrolateral/ventroanterior thalamic nuclei, relaying finally to the contralateral cerebral motor cortex - Guyton and Hall, p. 703. From there, the corticospinal (and rubrospinal) fibers descend and cross again at the pyramidal/ventral tegmental decussation (2nd decussation) before acting on the anterior horn motor neurons.

3. The two crossings cancel out, so the net motor influence returns to the same side. Because the cerebellar efferent pathway decussates twice before finally influencing the lower motor neurons, its ultimate effect falls back on the same side of the body from which the cerebellum received its original sensory input. Consequently, a lesion in one cerebellar hemisphere disrupts coordination, tone, and voluntary movement (ataxia, intention tremor, hypotonia) ipsilateral to the lesion, in contrast to a corticospinal tract lesion (which crosses only once) that produces contralateral deficits.