The family of an emotionally disturbed man who plummeted headfirst to his death when police stunned him with a Taser is suing the NYPD and the officers involved in the incident, including the estate of one who killed himself in remorse.

The family of Iman Morales, 35, is asking for $10 million in damages against the city, the New York Police Department, and Lt. Michael Pigott and Officer Nicholas Marchesona. The lawsuit also seeks additional training for police on stun guns and on dealing with emotionally disturbed people.

Pigott killed himself in October after becoming increasingly distraught over ordering Marchesona to use the stun gun during the standoff on Sept. 24 in Brooklyn.

The city law department said the lawsuit involves a very tragic case and it would review the legal papers thoroughly after it receives them.

It hasn’t been determined yet who will represent the officers, but the law department represents employees sued for acts within the scope of their employment.

The civil lawsuit filed Wednesday in state Supreme Court in Brooklyn claims the stun gun should have been used only as “a last resort.”

An amateur video of the incident was posted on Web sites and replayed frequently on news stations.

Witnesses and neighbors said Morales, who had a history of emotional problems, had become distraught and threatened to kill himself.

His mother arrived at his apartment to pick him up for a doctor’s appointment but he wouldn’t open his door. They argued, and someone in the building called 911. Police arrived and Morales 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 climbed down until he reached a ledge over a shuttered storefront.

Morales was teetering on the ledge and jabbing at police with a long fluorescent lightbulb when Pigott ordered Marchesona to fire the stun gun. The 50,000-volt shock immobilized Morales and he fell 10 feet and suffered fatal injuries. Officers had radioed for an inflatable bag, but it had not yet arrived at the scene when Morales fell.

“I asked them to please bring out an inflatable mattress, I was begging them, as a matter of fact,” his mother, Olga Negron said at a news conference Wednesday. “I even mentioned them, he has one inside the house, please just throw it out because my son’s going to get hurt.”

Negron, 55, and her two sons, Danny and Jessie Hernandez, ages 17 and 21, wore pins with a photo of Morales. Negron said she watched in horror as her son froze and fell to his death, and described him as a vibrant, intelligent man who had his medication changed the day he died.

Almost immediately after the death, police said the use of the stun gun appeared to violate department guidelines, which explicitly bar their use “in situations where the subject may fall from an elevated surface.” Pigott, who was stripped of his gun and badge and reassigned to desk duty after the incident, was found about a week later in a police locker room, dead of a self-inflicted gunshot wound.

Marchesona was reassigned to desk duty after the incident, but has since returned to the force and was promoted to detective. The investigation was closed.

After the incident, Police Commissioner Raymond Kelly appointed a new commander of the NYPD’s Emergency Service Unit, which responds to many incidents involving the mentally ill. He also ordered the unit’s 440 officers to get refresher training on how to deal with emotionally disturbed people.

Negron and her attorney, Seth Harris, reiterated their sympathy for Pigott’s family.

“I think all of our hearts go out to the lieutenant’s family and obviously the pain that he suffered … but it still wouldn’t detract from the anger that you might feel in the decision he made when it’s related to a loved one,” Harris said.