Generally you don't need a permit, but I get one anyway, especially if I'm shooting with a tripod. It's free and it takes less than a day, via fax. Here's the link: http://www.nyc.gov/html/film/html/pe...prcedure.shtml
Remember just becuse people get away with jay walking, doesn't mean it's legal. So you can go ahead and jay walk, just don't cite guidance from APUG as a defense.