Information About Occupying, Repairing, Or Replacing Sidewalks, Roadways, or Curbs

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In New York City, property owners must take care of the sidewalk next to their property, including the intersection corner quadrant, at their own cost.

This means:

You must follow Department of Transportation (DOT) specifications.

Penalties: If you do not take care of your sidewalk, you may receive a violation. You are encouraged to fix problems quickly to avoid more damage. DOT checks sidewalks when they get complaints. If your sidewalk is defective, you will get a Notice of Violation.

Permits: If you need to block the sidewalk or roadway (for example, for construction, filming, or placing dumpsters) you must get a permit from DOT.

NYC Department of Transportation (DOT)
http://www.nyc.gov/sidewalks
Sidewalk Permit