What is the legality of children conceived posthumously?

Last month, world news outlets carried the story of Pei Xia Chen, the wife of murdered New York policeman, Detective First Grade Wenjian Liu, who gave birth to their daughter over two and a half years after his death. According to reports, on the night of the murder, December 20th, 2014, and on the advice of medical practitioners present, Detective Liu’s wife requested that her husband's sperm be preserved. The couple had married a mere three months previous.