I found this on a web search:
Yes, a runny nose (rhinorrhea) can be a symptom of Parkinson's disease, affecting approximately 20% of individuals with the condition. This symptom is often more noticeable during or after eating, as well as at night.
Here's a more detailed explanation:
Cause:
The runny nose is often attributed to dysautonomia, a disruption in the body's autonomic nervous system, which can affect various functions, including nasal secretion.
Prevalence:
Studies have shown that rhinorrhea is more common in people with Parkinson's disease compared to those without the condition.
Impact:
This symptom can be socially embarrassing and lead to social withdrawal. It can also cause post-nasal discharge, coughing, or sneezing.
Other symptoms:
Parkinson's disease can also cause other non-motor symptoms, including drooling, difficulty swallowing (dysphagia), and changes in smell and taste.
Treatment:
While the exact cause of runny nose in Parkinson's is not fully understood, some nasal sprays may provide relief.
Important note:
It's crucial to discuss the symptom with a doctor to receive appropriate medical advice and treatment.
Runny nose and Parkinson's
Loss or reduction of smell (anosmia) is also common in Parkinson's and can be one of the earliest symptoms people notice. But research suggests that losing your...

Parkinson's UK
Uncommon Non-motor

I also have developed nasal drainage since being diagnosed. It's like clear water

Ruth, I don't have PD but I also have year around rhinitis (drippy nose). I get allergic and cold induced and exercise induced rhinitis The worst is when I'm exercising outside in early spring and it's cold. I blow my nose ever 2 minutes. Indoors and inactive isn't as bad. An ENT might be able to help you. I've never tried. I know that allergy pills and sprays were not very helpful.

I alsho have this

Constantly dripping nose for me ugh!!!!