No, I'm pretty sure people don't. In general, I think the attitude is to avoid parks at night. I would imagine that it's hard for police to maintain visibility that well when there's all kinds of bushes and trees in the way, not that much ambient light, and a lot of ground for them to cover.
I have also heard that Central Park has improved tremendously in the past decade.
Could that widespread belief perhaps have led to folks deciding not to go to the park after dark, though?
Or am I completely off-base? I'm not from NY (been there twice, and love it), so I have no idea. Do people go to the park after dark pretty regularly?