A schizophrenic subway rider who once claimed to have shoved a straphanger into the path of a train actually did it Monday — sending a 49-year-old woman tumbling to her death in Times Square, according to police. Cops took Melanie Liverpool-Turner, 30, of St. Albans, Queens, into custody moments after the gruesome tragedy on the 1 train platform. She was charged Monday night with second-degree murder for pushing Connie Watton of Queens in front of the train as it barreled into the 42nd St. station at 1:20 p.m, authorities said.(nydailynews.com)…[+]