A former NYPD detective was charged with raping a 14-year-old girl whom he snatched from a park bench on New Year’s Day, law-enforcement sources said.

Darrin Nemelc, 44, allegedly grabbed the teen after she ran away from her Brooklyn home, took a train to Manhattan and wound up hanging out near his home on Riverside Drive near West 155th Street.

Nemelc, who served on the force for seven years, grabbed the girl by her arm at 1 a.m. and ordered her into his apartment, where he attacked her, the sources said.