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.” Accused killer Rhamell Burke, 32, behaved erratically in 100 Centre Street Friday morning, a law enforcement source said. Obtained by NY Post 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.…