The backgammon-loving womanizer on trial for his wife’s murder moved out of the family’s Upper West Side home after he suggested an “open marriage” on their 10th wedding anniversary, according to court papers shown to jurors Thursday.

“I had absolutely no interest in such a sick and twisted concept, and no longer wanted to share a bed with the defendant,” victim Shele Danishefsky wrote in an affidavit filed just three months before she was found dead face-down in her bathtub on New Year’s Eve 2009.

Danishefsky, a UBS wealth manager, filed the affidavit to oppose paying $50,000 in maintenance requested by her scheming hubby, Rod Covlin.

After Covlin made the repugnant suggestion, she said she felt compelled to co-sign the lease for a studio across the hall in their luxury W. 68th St. building to get him out of her home.

The filing was introduced during testimony from her matrimonial lawyer, Lance Meyer, who described a contentious custody and divorce battle that was going in Danishefsky’s favor.

Meyer said that after the failed stockbroker falsely accused Danishefsky of sexually abusing their then 2-year-old son, Myles, a matrimonial judge curtailed his visitation.

She also ordered that future visits with Myles and his sister, Anna, be supervised.

After the judge issued the custody decision in late July 2009, Meyer said he spotted an enraged Covlin arguing with his divorce lawyer outside the courtroom: “Their voices were raised, he was in his attorney’s face,” he said.

Later that month, Covlin was fired from his $125,000 a year job and argued in court papers that he couldn’t afford child support.

But Danishefsky countered that he was spending more than a $1,000 a month to compete in backgammon tournaments.

The matrimonial judge eventually told Covlin that if “you can’t pay child support then you certainly shouldn’t be playing backgammon” and banned him from pursuing his beloved hobby, according to Meyer.

The divorce continued to go downhill for Covlin, and about a month before the murder, a judge not only denied his maintenance request but ordered that he pay $425 a month in child support.

Covlin’s friend and colleague at the brokerage firm Pragma Securities, Marshall Baron, told jurors that the defendant was fired in 2009 for playing online backgammon instead of doing his work.

Baron said that before Covlin separated from his wife he’d boast about his mistresses and even mentioned meeting women on backpage.com.

But the witness told jurors in Manhattan Supreme Court that he had little tolerance for that kind of chatter. “If your wife and family can’t trust you, why should I?” he said he once told Covlin.

The deranged hubby allegedly admitted to Baron that he was spying on his wife and had installed a keystroke logger on her computer.

Assistant DA Matthew Bogdanos has argued that Covlin snapped Danishefsky’s neck then made it look like a bathtub slip and fall to get his hands on her $5.4 million fortune.

Defense lawyer Robert Gottlieb told jurors Danishefsky’s death wasn’t murder but a tragic accident.

The trial continues Monday before Justice Ruth Pickholz.