[36 N.Y.2d 230 Page 235] On this appeal we are called on principally to consider the doctrine of harmless error as applied to errors which occurred on defendant's second trial. In this case a mother was charged with criminal responsibility in connection with the deaths of her son and her daughter. On her first trial defendant was charged only with the death of the daughter and was convicted of manslaughter. On appeal this conviction was reversed and a new trial was ordered. (People v. Crimmins, 33 A.D.2d 793, affd. 26 N.Y.2d 319.) On her second trial the jury convicted defendant of murder of her son and manslaughter of her daughter. The Appellate Division then reversed the conviction of murder of the son and dismissed the charge against defendant with respect to his death. (People v. Crimmins, 41 A.D.2d 933.) As to the manslaughter conviction, the Appellate Division also reversed defendant's conviction but ordered a new trial with respect to her responsibility for the death of her daughter. The case is now before us on appeal by the People.