Cholesterol is so important for brain health that the brain has its own synthetic machinery for making it.
The brain is only 2% of body weight yet contains as much as 25% of the body's cholesterol.
Blood levels of total and LDL cholesterol are lower in Parkinson's disease patients.
Ferritin (iron) levels are higher.
[PMID: 21282940]
Some statins, those that are lipophilic, can penetrate the blood brain barrier.
The effects of these statins has been described as "pleiotropic", meaning they do lots of things; since they lower cholesterol, presumably many of these things are not good.