The schizoid symptoms you described would be caused by medications rather than Parkinson’s disease itself because in PD there is a lack of dopamine producing neurons and in Schizophrenia there is an "excess" actually an oversensitivity of certain dopamine receptors.

So the symptoms would have to come from medications which impact the elimination of dopamine, prevents Vitamin B6 from destroying dopamine, blocks the conversion of levodopa, increases the release of dopamine, amplifies the effects of DA, activates dopamine receptors.

There are however other personality changes which can occur to a PD patient which might be construed as something akin to schizophrenia.

Many PD meds can produce hallucinations and delusions. Some will stop if the dosage is reduced or discontinued; some will only abate to a limited extent.

There are also medications used to treat Parkinson’s depression which can have some powerful effects especially when prescribed with certain anti-parkinson’s meds.

Glutamate hyperactivity may also play a role in the symptoms you describe. The glutamate/dopamine homeostasis is upset in PD.

The fact people being treated for Parkinson’s with meds to improve to usable levels of dopamine in the brain can become psychotic. By the way, people being treated for schizophrenia can experience movement problems.

resources:
http://www.ncbi.nlm.nih.gov/pubmed/9849144
http://www.ncbi.nlm.nih.gov/pubmed/1350197?ordinalpos=1&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_SingleItemSupl.Pubmed_Discovery_RA&linkpos=3&log$=relatedreviews&logdbfrom=pubmed