The homeless career criminal accused of randomly assaulting an NYU student on her way to class committed an eerily similar attack just days earlier in Manhattan, cops said Wednesday.

James Rizzo , 45 — who has 16 prior busts on his record — allegedly shoved a 68-year-old woman as she walked on Fifth Avenue near West 47th Street at around 8:45 p.m. on Thanksgiving Day, police said.

Rizzo is accused of striking the victim with his elbow, without warning, so violently that she fell to the ground and suffered a small cut, according to cops.

The unhinged perp’s spree continued Monday morning, when he allegedly came up behind 20-year-old Big Apple coed Amelia Lewis on Broadway near Astor Place, slapped her head and buttocks and pulled her hair in a shocking attack, police said.

He was c

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