This article "Constipation in neurological diseases" has some info on the subject and also some possible strategy for management and drug treatment in constipated patients.

"The pathophysiology of constipation in PD seems to be multifactorial. Lewy bodies have been found in both parasympathetic nuclei and nerves, including the vagal nucleus and myenteric plexus from upper oesophagus to rectum,26, 27 indicating a genuine autonomic failure with a pathoanatomical basis. This is consistent with neuropathological studies, in which histological changes were found in the corresponding areas28, 29 with Lewy bodies in both CNS as well as degeneration and depletion of dopaminergic neurones of the myenteric and submucosal plexus27, 30, 31"

http://jnnp.bmj.com/content/74/1/13.full

it is interesting to note that James Parkinson recognized gastrointestinal features in his original monograph published in 1817.