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STICKUP BACKFIRES

An off-duty Bronx cop shot and killed a man trying to rob the officer’s wife of $20,000 in gambling winnings she was holding for a jailed man, police sources told The Post.

Officer Nadin Perez chased the robber through the third-floor hallway of his Bedford Park building and down the stairs Saturday night, firing several shots and wounding the man.

Carlos Rios, 47, who had ambushed the woman and her 3-year-old daughter in the building’s elevator, died at Montefiore Hospital.

Rios somehow had learned that the officer’s wife, Jeanette, was holding money for a man who had won an illegal lottery patronized by Dominicans but was now in jail, the sources said. The money is now in police hands, the sources said.

It wasn’t immediately known how Jeanette knew the jailed man.

Cops said Rios had followed her and her daughter into their building on East 201st Street shortly before midnight.

After stepping into the elevator, Rios and the woman both pressed a button for the same floor.

She asked Rios whom he was visiting, and he said he had made a mistake, and pressed another button.

But when she and her daughter got out, Rios pulled out a 9mm pistol and grabbed them from behind, cops said.

Rios told her to open her apartment door, but she and the girl screamed for help, and her husband, a 10-year NYPD veteran, ran to the rescue.

Witnesses said Perez, 43, sprinted out of his third-floor apartment with nothing but his boxer shorts and 9mm off-duty weapon.

“I saw her go in the elevator,” neighbor Orsa Omar said. “The guy was so close to her I thought they were together. I hung out in lobby a while and saw the cop running down the stairs after the man.”

Witnesses told cops that Perez identified himself as an officer before firing at Rios.

Rios fled outside onto Perry Street, where he ditched the gun in the unlikeliest of places – the wheel well of the cop’s car parked nearby, another source said.

Witnesses said Rios then tried to hide under a parked minivan but was yanked out by cops who responded to the 911 calls.

Rios had only one prior arrest for drunken driving, police sources said.

Perez and his family were taken to St. Barnabas Hospital for evaluation but apparently had no injuries.

His daughter was spotted yesterday playing in a park with a relative.

Officials said Perez fired seven shots. Perez initially told cops that Rios shot at him, but no bullets fired from his gun were found, sources said.

Eleven live rounds were found inside Rios’ gun, including one in the chamber.

Neighbor Peter Girvan said Jeanette’s screams were “blood curdling.”

“All of a sudden, he ran down the stairs, and I saw my neighbor, the cop, chasing him,” he said.

“I ran and called 911, and I heard a shot in the hallway. I yelled to my wife to get into the bathtub in case there was a stray bullet.

“Then I heard at least seven more gunshots. I was pretty scared.”

“I was standing in the hallway with a few neighbors when the cop came back with his weapon in his hand,” Girvan said.

Officials said Perez is assigned to the Midtown South Precinct and is also a Coast Guard veteran.

cj.sullivan@nypost.com