I am not sure there is a strong connection, but studies have given some hints.
( I have it, both my parents had it)
Studies are showing there is a link to people who eventually develop Parkinsonism, both to RLS , and in different studies, to autism.
All of it is neurological in basis, and all of it is suspected to be genetic, although in each diagnosis, no actual gene for RLS, Parkinson's, or autism has been found. RLS is also called Willis Ekbom disorder/disease/syndrome.