26-year-old Sungjae Song is a South Korean citizen who lives in Palisades Park.
Police say last month, he broke into a home and climbed into bed with a stranger and asked to spend the night.
She started screaming and fled.
Police say he is suspected in five other incidents, including grabbing a woman's arm on the street.
Song faces multiple charges, including aggravated criminal sexual contact.
He was arrested after a borough resident reported an incident and then viewed the composite sketch that had been made, police say.