They say 62-year-old Roberto Marcucci turned himself in Wednesday night.
Marcucci is accused of walking into a 68-year-old woman's room and touching and kissing her on Monday.
Investigators say another patient called a nurse, and Marcucci ran away.
Marcucci has three prior minor arrests for drug possession, assault and petit larceny. He is now facing a charge of sex abuse.
NYC Health and Hospitals released a statement saying, "At NYC Health + Hospitals, the safety of our patients and staff are our first priority always. Our staff immediately reported the incident to NYPD, shared the security video, and are assisting with the investigation."
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