The Manhattan district attorney’s office has opened a criminal investigation into a fatal crane accident on the East Side, focusing on whether a part of the crane had been seriously damaged last year and then inappropriately put back into service, an official involved in the investigation said on Saturday. The piece in question is a rotating apparatus, or turntable, that connects the operator’s cab and the boom to the crane tower. The official said investigators believed but were not certain that the turntable involved in Friday’s accident, on East 91st Street, was damaged during construction on West 46th Street last...