Officer Peter Ciollo, 29, is accused of having sex with the teen relative at his Staten Island house on the Fourth of July.
The victim is reportedly his sister in law's sister or other immediate relative on his wife's side of the family.
Authorities say Ciollo gave the girl alcohol to drink, then let her drive his car around the neighborhood.
Then they returned to his home, where he allegedly showed her computer porn before they started touching each other in his bed.
The girl says she doesn't remember what happened next, but she told police that when she woke up, she was in the bed and Ciollo's wife had walked in on them.
A wedding notice in the Staten Island Advance says he was married in 2009.
Ciollo is charged with attempted rape, endangering the welfare of a child, sexual abuse and unlawfully dealing with a child-alcohol. He has been an officer since 2006, assigned to the 120th Precinct.
He has been suspended without pay.