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 2371, Chakotay told B'Elanna Torres that she had come close to driving some of the bones in Joseph Carey's nose into his cerebellum when she hit him. (VOY: "Parallax")
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")
Later that year, The Doctor used undamaged chromosomes from Denara Pel's cerebellum to create a DNA profile, which then allowed him to program a holographic body for her. (VOY: "Lifesigns")