Eye witnesses to the collapse on Friday morning said that the crane's jib came away from the tower at the point where the cab was connected to the crane.
Investigators were considering the possibility that welds to the slewing ring assembly were cracked or had become so.
The crane fell into a 23-storey block crushing the top apartment block. The driver of the crane and a construction worker below were killed. Another was seriously injured.
The collapse is the second in the city this year. In March six workers died after a tower crane's 61m high mast broke free of the building it was attached to, crashing into an apartment block on the other side of East 51st Street (NCE 20 March).
The crane's height was being increased at the time. It is unclear at this stage whether Friday's accident occurred during a similar self erecting operation.
Circumstances surrounding last week's collapse are being investigated by the City's District Attorney office.
The District Attorney's office confirmed that recent repairs made to the crane would be examined "among many other things" but would say nothing more definite at this stage.
Fire Department and city Building Department officials are also investigating the incident.
The crane was used for construction of a 35 storey apartment block on the junction of 2nd Avenue and 91st Street in the exclusive Upper East Side of Manhattan.
Work had reached around the 10th floor. The crane was supplied to the project by the New York Crane & Equipment Corporation. The company refused to comment on the incident.