Home invader asks woman to stay the night

(INSIDE EDITION)--A New Jersey woman got a terrifying surprise when cops say a man broke into her home and crawled into her bed as she slept.

And if that wasn't enough to make her skin crawl, the woman says the home invader than asked her if he could spend the night.

The woman's screams scared the intruder away, police in Palisades Park say.

Cops added that the suspect has likely stalked women before.

The potential serial stalker is alleged to have followed a woman into her building earlier this month before knocking on her door while making sexually charged comments.

A third woman told cops she was walking down the street when a man stalked her and then stood next to her house.

And finally, another woman said she was walking down Roosevelt Place near a Shop Rite when the same man reportedly stalked and stood outside her home.

The woman's brother got in his face, prompting the perpetrator to claim he was lost, police say.

The incidents all occurred in the same immediate area and each woman described the suspect as a white male in his 20s, approximately 5'10" tall.

The women helped police create a sketch, which has been released to the public. Anyone who recognizes him is asked to call the cops.

Meanwhile, police believe the suspect was able to enter the woman's home June 18 through an accessible open door or window and have asked women in the area to make sure their residences are securely locked.