The recidivist madman accused of fatally shoving a retired Big Apple teacher flashed a killer smile in his first court appearance Saturday to face second-degree murder charges in the case.

Rhamell Burke, who’s been arrested four times since February, showed no remorse at his Manhattan Criminal Court arraignment for the random attack against retired teacher Ross Falzone.

The suspect, clad in a black sweatshirt and holding a surgical mask while his hands were cuffed behind his back, seemed giddy as he stood before Judge Linda Capitti.

Burke, 32, had been taken to Bellevue Hospital in handcuffs by cops around 3:30 p.m. Thursday as an “emotionally disturbed person,” but was allowed to leave an hour later.

That evening he was caught on video as he followed the 76-year-old victim near a Chelsea subway station, according to a Manhattan prosecutor who called the attack “completely unprovoked.”

Falzone is seen slowly walking towards the subway entrance at the 18th St. 1 train station with Burke walking behind him, the footage shows, officials said. 

Burke then allegedly uses both hands to shove the unsuspecting victim down the stairs, according to the prosecutor.

The judge ordered Burke remanded and called him a flight risk. 

“Anything else, judge?” Burke, who did not enter a plea, bizarrely asked Capitti as he was led out of the courtroom.

On Feb. 2, Burke was accused of petty larceny for opening a bag of chips at a Duane Reade at One World Trade Center and trying to leave without paying, police sources said.

When Port Authority cops responded, he assaulted three of them, leaving them with cuts and shoulder injuries, prosecutors said Saturday as they read his existing cases in court.

He was charged with assaulting the officers and initially taken to Bellevue — but later given supervised release, records and sources said.

Just two weeks later, on Feb. 14, Burke was arrested again in a bizarre case in which officers responded to a call of a man carrying a shovel at the No. 1 subway station on Seventh Avenue and West 23rd Street in Chelsea, police sources said.

Police who responded were told Burke — who sources said used the name Byron Cherry — kicked in an MTA subway scrubber room door, stole the shovel and used it to smash several car doors. He also threw a trash can onto the tracks, which later caused one train to go out of service.

Burke was also arrested on Feb. 25 in Brooklyn, this time for resisting arrest, obstructing governmental administration, weapons possession and drug charges after sources said cops found him lying on a subway bench and taking up multiple seats on a C train.

He allegedly held onto a train pole and kicked officers as they tried to cuff him, the sources added.

Cops allegedly found Burke with a large kitchen knife, a crack pipe and a syringe with narcotics — but was still released on his own recognizance.

He was charged with criminal mischief and reckless endangerment in the shovel case and again given supervised release, but later missed a court date in March, sources said. A bench warrant was issued and but vacated when he showed up to an April 6 appearance.

On April 2, he allegedly attacked a woman on a subway car and was charged with third-degree assault — but the woman declined to cooperate with prosecutors, she later told The Post.

In that case, prosecutors requested $3,000 cash or $9,000 bond but Judge Marva Brown freed him on supervised release.

Brown, a former Legal Aid Society attorney, is best known for causing a firestorm after she released Amira Hunter in February 2024 after Hunter was accused of smashing a water bottle onto the head of cellist Iain S. Forrest as he performed in the Herald Square Station.

Falzone’s neighbor, Ivy Vega, told The Post she was gutted over the death of her “very kind” friend. 

“It’s a tragedy on both ends, the fact that, Ross, had to die in such a senseless way,” the 33-year-old said. 

“But I think it’s also a tragedy that’s a failure of the system. Mental health issues, and mental health crises are very real issues in the city, across the country, in the world.”