The cerebellum was a part of the brain that played an important role in the integration of sensory input and motor output.
In 2367, when Deanna Troi temporarily lost her emphatic sense due to the influence of two-dimensional lifeforms, a pattern of unresponsive neural cells was recorded in her cerebral cortex and cerebellum. (TNG: "The Loss")
In 2372, prior to his warp 10 flight, The Doctor detected an enzymatic imbalance in Tom Paris' cerebellum that had a small chance of causing a brain hemorrhage under subspace stress. (VOY: "Threshold")
While Chakotay was hallucinating when the USS Voyager was trapped in chaotic space in 2375, a vision of The Doctor told him that an upper cut would cause the head to snap back, rupturing tissue in the cerebellum and upper spinal cord. (VOY: "The Fight")