Central park scene

I was in NYC in late August, and for the first time, really went into Central Park. I had been in there before, but only for like, 5 minutes--unlike this time where we walked around the whole place. I wish I knew where in the park the scenes were shot, like Miss Piggy tackling the purse snatcher (and chasing him on rollerskates). Anyone know? A lot of other movies (older than this one) have every single filming location, like Grease for instance. We walked down to the lake by where they have boat rentals, and into Sheep's Meadow. We also saw the Afrobats do a show right by Bethesda Terrace, somewhere along Terrace Drive right by the stairs. I swear I saw these guys do the same show in Battery Park back in 2005.
Anyone have any idea where exactly they shot in Central Park? The thief runs down some stairs but it didn't look like the stairs leading down to the Bethesda fountain.

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