NEW YORK, Feb 10 (Reuters) - New York City's consumer protection agency has sued Extra Space Storage EXR.N, accusing the self-storage company of employing bait-and-switch pricing and other "predatory" practices, and allowing storage units to suffer from vermin infestation, water damage and mold.

The complaint filed by the New York City Department of Consumer and Worker Protection seeks full restitution for consumers and more than $5 million in penalties, the agency said on Tuesday.