The wife of an NYPD precinct commander lied to upstate cops when she claimed she was beaten outside the couple’s Rockland County home on Valentine’s Day, police sources said yesterday.

Her story led Deputy Inspector John D’Adamo, commanding officer of the 52nd Precinct in The Bronx, to admit to Clarkstown cops he had an affair with a female officer, who was also in another relationship, the sources added.

Investigators initially believed that the attack, and the slashing of the inspector’s car tires, were the result of the love triangle.

But D’Adamo’s wife, 40, confessed to concocting the account once detectives noticed her injuries weren’t consistent with the severity of the beating she described, according to the sources.

Police now believe her injuries were self-inflicted.

The woman was undergoing psychiatric evaluation, the sources added. There are no plans to charge her.