From the perspective of research studies alone it would be difficult to give any firm recommendations for acupuncture as a treatment of Parkinson's Disease. There are a number of studies, some undertaken in the US but the vast majority in China, which show some positive signs, but not of sufficient change in a significant number of patients under study to draw any firm conclusions. You can see some of the studies if you google 'ncbi acupuncture parkinson's disease' - the National Centre for Biotechnical Information in the States is a convenient way to find many of the the more significant papers. There is also a Cochrane Review of a protocol for assessing the value of acupuncture, but as far as we are aware this has not been put into action yet.
With all chronic degenerative conditions the extent to which acupuncture can help has to be carefully explained. It is often, as one rather ironic patient said, a case of 'getting worse slower', and this is extremely difficult to quantify in a condition like Parkinson's where the disease progression is neither smooth nor predictable. Anecdotally there are many accounts of patients finding that treatment helps with some of the manifestations of the disease, such as the periods of rigidity and freezing, and a general sense of well-being, but these are not documented sufficiently well to be able to claim any undisputed levels of efficacy.
The best course of action is to see whether a BAcC member local to you will give you an honest assessment from an eastern perspective of what they might be able to achieve for your own unique patterns. There may be elements of how the condition manifests which they may feel that they can help.