The maniac accused of pushing a 76-year-old man down a flight of Manhattan subway stairs to his death appeared in an NYC court just hours after the heinous attack — and strolled out, because no one realized he was the killer, The Post has learned.

Rhamell Burke acted crazy when he showed up Friday morning at Manhattan Criminal Court for a hearing on a third-degree assault case, sources and records showed.

“He was acting like a nut all morning,” a law enforcement source said. “Even if they didn’t know he was a suspect, what kind of system lets a guy acting like that just walk out without an evaluation of any kind.”

Burke, 32, was at one point walking with his hands up as if he were surrendering, a screenshot of surveillance video obtained by The Post shows. 

He appeared before Judge Elizabeth Shamahs at a 9 a.m. hearing on a third-degree assault charge, records show. His case was adjourned and he left the courthouse about two hours later. 

The evening before, authorities said, Burke had followed retired teacher Ross Falzone near a Chelsea subway station before suddenly shoving the 76-year-old down the subway steps, killing him.

“They didn’t know he was the perp,” a police source said of Burke’s court appearance the next day in the other case.

Two detectives with the NYPD’s Warrants Division who were working transit overtime later saw him walking into Penn Station and grabbed him in relation to Falzone’s death, police sources said.

Burke — who has been arrested four times since February — had been released from Bellevue Hospital’s psych ward five hours before he pushed Falzone at 18th Street in Chelsea.

Cops had brought Burke to the hospital as an “emotionally disturbed person” around 3:30 p.m., according to police. The label is given to mentally unstable people who are picked up by cops for acting erratically.

Officers encountered him acting erratically outside the 17th Precinct stationhouse on East 51st Street. He allegedly pulled a stick from the garbage and held it as he approached them, police said.