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Pop-music icon Paul Simon and his singer wife Edie Brickell were busted on disorderly conduct charges after they got into an ugly pushing match in their tony Connecticut home Saturday night, cops said.

But the couple was all lovey-dovey during a court appearance Monday, holding hands, telling a judge they get along fine and insisting that the dispute — which escalated into pushing and shoving — was “atypical.”

Sources said Brickell, 48, started the argument with Simon, 72, in a cottage on their property in New Canaan, a Fairfield County town about 45 miles from Manhattan that’s one of the wealthiest in the US.

Brickell admitted as much in a statement released by her and her husband’s lawyer, Allan Cramer.

“I got my feelings hurt and picked a fight with my husband. The police called it disorderly. Thank God it’s orderly now,” she said.

Cops responded about 8:20 p.m. after getting a 911 hang-up call from the couple’s $17.6 million home on Brookwood Lane — which Cramer said may have been placed by Brickell’s mother, Mary, who was visiting.

Cramer said after the argument started, Simon tried to leave the cottage but his 6-inch-taller, younger wife blocked her aging hubby’s way and then gave him a shove, which he returned.

“She wanted to talk about something, and Paul didn’t want to talk about it. Paul wanted to exit,” Cramer said, adding that one of the couple’s three children often stays in the cottage.

“Edie Brickell is from Texas, and he is from Queens. And you know what? Things are done one way in Texas, and there’s another way of doing things in Queens,” he said. “Paul’s the kind of guy who thinks things will settle themselves. Edie wants to settle things right now.”

During a brief appearance in Norwalk Superior Court, the Rock ‘n’ Roll Hall of Famer and his wife both told Judge William Wenzel that they did not feel threatened by the other.

“Both of us are fine together. We’re going home together, and we’re going to watch our son play baseball,” said Simon, who entered court holding Brickell’s hand and didn’t let go throughout the five-minute hearing.

“We had an argument which is atypical of us. Neither of us has any fear or any reason to feel threatened. I don’t feel like I need to be protected,” said Simon, wearing a navy-blue suit.

“He’s no threat to me at all,” added Brickell, clad in brown skinny pants, a black blazer and ankle boots.

Wenzel declined to OK a protective order — which had been requested by the court’s Family Services office — unless there is further violence between Monday and May 16, their next court date.

Cramer said outside court that the domestic incident was “much less than nothing” — but admitted the argument did turn physical.

“I think there were a couple of pushes,” he said, adding he did not know what they were fighting about.

Before the hearing, Cramer — who also reps Rolling Stones rocker Keith Richards — objected to the presence of cameras in the courtroom.

“These are people, very well-known people,” he said before the judge cut him off.

Wenzel shot back, “Everyone gets the same treatment, whether you’re just getting off the street or a media star.”

Later, Cramer called the media hullabaloo “the price of celebrity. It was such a minor situation. If it was Joe Blow, you certainly wouldn’t be here.”

New Canaan Police Chief Leon Krolikowski said during a news conference that Simon and Brickell suffered “minor injuries’’ and that there was “aggressiveness on both sides.’’

Neither was taken into custody, Krolikowski said, but were issued misdemeanor summonses. Since they were not processed at police headquarters, neither their fingerprints nor mug shots were taken.

Simon agreed to leave and spend the night at his apartment in Manhattan on Saturday, cops said.

“Frankly, they were both victims,” Krolikowski said, noting that there has been a spike in family disputes in the super-rich town — which CNN ranked the fifth highest-earning community in the US in 2013, with a median family income of $236,758 — likely because of recent hard economic times.

“It concerns us. It’s good if people are calling us and asking us for help. We do want people to call us and ask us for help,” the chief said.

The Simon and Garfunkel legend and Brickell, who gained fame with the 1986 hit “What I Am,” married in 1992. They have two sons, 16 and 21, and a 19-year-old daughter.

Police did not say whether any of the children were home during the dispute, though Cramer said they might have been.

Sources said the couple has been under stress because she has been in rehearsals for the Broadway musical “Bright Star” with Steve Martin, and that Simon had recently returned from a tour with Sting.

Simon has won 12 Grammys, and has three “album of the year” awards under his belt for “Bridge Over Troubled Water,” “Still Crazy After All These Years” and “Graceland.”

He is also a member of The Songwriters Hall of Fame and the Rock ‘n’ Roll Hall of Fame — as half of the duo of Simon and Garfunkel and as a solo artist.

Brickell is famed for her 1988 debut, “Shooting Rubberbands at the Stars,” with her band at the time, the New Bohemians.

NCAdvertiser.com was first to report the news.

Additional reporting by Sophia Rosenbaum