Cerebellar hypotonia is brought about when there is damage to the deep cerebellar nuclei. Interestingly, it is not usually manifest as muscle weakness, only decreased muscle tone.
Under normal circumstances, the deep cerebellar nuclei send 'reinforcing' signals to the motor cortex and brain stem motor nuclei. This is via the cerebellocortical tract, and serves to increase the tone. Thus, if the deep nuclei are lost for any reason, there is an initial slight decrease in tone. (After a few months though, the motor cortex compensates by increasing its intrinsic activity, and the hypotonia disappears.)