I've found multiple sources claiming that damage or impairment as a result of alcohol to the vermis of the cerebellum results in speech impairment. I find this a bit surprising, since the only areas I know that are used for speech production are Broca's area. Additionally, I don't know of any way that the vermis influences this area or any other facial nerve that may need co-ordination to produce speech.
So why does damage/impairment of the vermis result in dysarthria?