Severe mental impairment , not sure having Parkinsons means you automatically have this type of disability. Physical disabilities are a separate issue.
The word severe implies that you would not be able to function on a social or intellectual level. If you have mental health issues perhaps discuss this with your PD nurse, specialist to explore whether your difficulties can be classed as 'severe'. Benefits are awarded to those who meet the criteria and Parkinsons is a so called 'boutique' disease, not everyone will experience the same symptons.
Best ask the council for clarification, but thinking logically you would need to provide evidence for the mental health issues you have rather than a statement of a PD diagnosis.