You can place leaves, grass clippings and small twigs (less than 1/2 inch in diameter) curbside for collection by the NYC.
There is no limit to the amount of clippings that can be put out for collection provided they were produced by residents as household waste. In all boroughs throughout the year they can be placed in the following:
Black or dark brown bags
Unlined trash containers
Twigs and branches greater than 1/2 inch in diameter cannot be mixed with leaves and grass clippings. Any leaves or grass clippings from yard work done by a private contractor must be removed by the contractor.