A uniformed cop has told investigators his partner – who stands accused of rape – had sex with a drunken woman in her East Village apartment after the on-duty officers escorted her home, sources said yesterday.

Officer Franklin L. Mata is insisting that the woman willingly agreed to sex with married Officer Kenneth Moreno, 41, last Dec. 7 as the young partner stood by, sources told The Post.

But investigators don’t buy that story, which Mata has conveyed through his lawyer, sources said.

“The working theory as of now is that it was not consensual,” said a source familiar with the probe by the Police Department’s Internal Affairs Bureau and the Manhattan DA’s sex-crime unit.

Investigators have proof the woman was “falling-down drunk,” and thus incapable of consenting to sex, sources said. That proof includes statements by witnesses who saw the woman earlier and a surveillance video showing one cop supporting her arm as he guides her into the East 13th Street building.

Under the law, if a person has sex with someone who is incapacitated, the person can be found guilty of rape.

Both cops have been placed on modified duty and stripped of their guns and badges.

Doris Greenberg, the alleged victim’s landlady, said she was “livid” that the cops haven’t been arrested.

“Those two ought to be castrated for what they did to this poor girl,” Greenberg said.

Sources said the woman was out drinking with friends Dec. 6 and got very drunk before taking a cab home.

The cabby, concerned because the woman was drunk and vomiting, called 911. Moreno, a 17-year veteran who has two kids, and Mata, a three-year vet in his 20s, arrived and escorted her up to her apartment at about 1 a.m.

Surveillance video from a nearby bar shows the cops leaving about seven minutes later, according to bar owner Heather Millstone. The tape shows the cops returning about 40 minutes later – and staying inside for 20 minutes before leaving and doing their best to avoid the surveillance camera, Millstone said.

The cops entered the building a third time – using a key belonging to the woman – at about 3 a.m., this time out of camera range, Millstone and sources said. It was during that last visit that Moreno allegedly raped the woman, sources said.

Additional reporting by Murray Weiss

brad.hamilton@nypost.com