Officers had radioed for an inflatable bag as the incident unfolded, but it had not yet arrived at the scene when Morales fell.
"None of the ... officers on the scene were positioned to break his fall, nor did they devise a plan in advance to do so," said chief department spokesman Paul Browne.
The lieutenant who directed the use of the stun gun was stripped of his gun and badge, and the officer who shocked Morales was placed on desk duty as the investigation continues. Their names were not released.
Witnesses and neighbors said Morales had become distraught and threatened to kill himself Wednesday. His mother called 911. When police arrived mid-afternoon, he fled naked out the window of his third-floor apartment to the fire escape. He tried unsuccessfully to get into an apartment on the floor above, and then clambered down until he reached a ledge over a shuttered storefront, where he started jabbing at officers with an 8-foot-long fluorescent light.
An amateur video posted on the Web site of the New York Post shows one of the officers raising a Taser at Morales, who freezes and topples over headfirst as the crowd screams.
The man's death renewed focus on the use of stun guns by the NYPD. Thousands of city police sergeants began carrying Tasers on their belts this year after the department expanded use of the weapons. The pistol-shaped weapons fire barbs up to 35 feet and deliver 50,000-volt shocks to immobilize people.
Browne said the guidelines issued with the expansion in June specifically state that when possible, the stun guns "should not be used ... in situations where the subject may fall from an elevated surface."
Officers are allowed to use Tasers if they believe emotionally disturbed people are a danger to themselves or to others.
The NYPD receives more than 80,000 calls annually in such circumstances and uses stun guns about 300 times on average. So far this year, stun guns have been used 180 times. No other deaths have been reported.
The department has used Tasers since 1984, but policy previously called for sergeants to store the stun guns in their trunks while patrolling. Police Commissioner Raymond Kelly acknowledged that the weapon is considered controversial, and some organizations want the weapons banned.
Mayor Michael Bloomberg initially declined to comment on the death, but when asked by a reporter Thursday whether such incidents would make people afraid to call police in cases of emotionally disturbed people, he responded, "You should never be afraid to call the police."