There are many factors which go into determining whether someone has or does not have legal capacity. Can they understand and appreciate the nature of their condition and the impact which it has on their life? That's the primary guiding question, and it's answered by asking the alleged incapacitated a lot of questions and seeing how they answer the questions (do the answer make sense or can the person even understand the question?). The court evaluator will speak to the person's family and nursing staff and attending physicians and gather medical records, in most cases, and see if the MD wrote "dementia" or "bi polar disorder" on the medical chart. Can the alleged incapacitated person balance their checkbook? Do they know and appreciate how much income and expenses they have every month? So there are a whole lot of factors along these lines which go into determining whether someone has legal capacity under NY law.
