Why is the vermis of the cerebellum associated with speech? 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?

Although speech production is in generally executed in the cerebral domain, the dysarthria resulting from damage of the vermous is a symptom of the resulting general muscle weakness. So yes, you get slurred speech because your muscles are weak, but the weak muscles certainly aren't ever isolated to speech production.