People with REM sleep behavior disorder often act out their dreams with violent movements.
Multiple system atrophy is a disorder that causes symptoms similar to Parkinson's.
Of the participants, 13 were diagnosed with dementia, 13 others were diagnosed with Parkinson's and one was diagnosed with multiple system atrophy.
The study found that the time between when the sleep disorder begins and the neurological symptoms showed up ranged up to 50 years.
"More research is needed on this possible link so that scientists may be able to develop therapies that would slow down or stop the progression of these disorders years before the symptoms of Parkinson's disease or dementia appear," said study author Bradley F. Boeve, MD, in a news release.
The findings are published in the online issue of the medical journal, Neurology.