It happened near Tompkins Square Park in the East Village before dawn on Wednesday.
The woman tells police the man entered her apartment and went to lie down next to her.
She says she awoke and chased the man off. He fled.
The woman was not injured.
The suspect was described as 5 feet 9 inches tall, weighing about 170 pounds, and was wearing a blue hat, glasses, a black-hooded sweatshirt with a black and white jacket, beige sweatpants, and light-colored shoes.
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