A backgammon whiz accused of murdering his estranged banker wife told cops he pulled her body out of the bathtub and tried to resuscitate her — but his clothes were ​bone ​dry, an officer testified Tuesday at a hearing.

Less than an hour had elapsed since Rod Covlin, 44, had found his wife, Shele Danishefsky, face-down in the tub of her apartment and called cops.

“How did his clothing appear when you encountered him?” defense lawyer Derrelle Janie asked Sgt. Yadelie Sanchez. “His clothing was dry, correct?

“Yes,” she answered. She said Covlin had just explained to her and her supervisor what had happened.

He’d gotten a phone call from his panicked 9-year-old daughter Dec. 31, 2009, saying something was wrong with her mother.

He rushed across the hall to the apartment where his wife and kids had been living since the split and made the grisly find.

Sanchez said Covlin even offered a theory as to how she died. “She was trying to grab some​​thing, a piece of wood broke, and she landed in the bathtub and hit her head,” she recalled Covlin telling her.

She said he was so distraught that he was shaking and gagging and even hugged her supervisor.

Covlin had been in the presence of cops from the time they arrived on the scene to when he spoke to Sanchez.

The strange detail about the dry clothing, which emerged for the first time during the two-day hearing, could mean that Covlin changed his clothes before cops showed up.

The defense argued that statements Covlin made to cops shouldn’t be admissible at trial because they weren’t made voluntarily.

Prosecutor Matthew Bogdanos countered that at the time Covlin spoke to the police, the Upper West Side apartment wasn’t a crime scene and the case wasn’t yet a homicide.

Although Covlin was a longtime suspect, he was only arrested two years ago after allegedly blabbing to his girlfriend about what he’d done. He was just two months away from inheriting half of her $4 million fortune.

An autopsy conducted three months after Danishefsky’s death determined that a bone in her throat had been broken by force.