Officers were called to the apartment block in Western Sydney on Friday evening following a distressed call from a 46-year-old woman reporting an intoxicated man straddling her balcony.
Police say the man was still on the balcony as they arrived and officers immediately began urging him to return to safety.
The 55-year-old reportedly lost his footing and fell to the ground at the same time as some police started running up the stairs while others stayed below the unit.
Paramedics treated his critical head injuries but he was unable to be revived and died on the scene.
A crime scene has been established in the Fairfield location and a critical incident declared.
A specialist team from the Auburn Police Area Command is set to investigate the incident and the probe will be independently reviewed by the NSW Police Professional Standards Command and the law enforcement watchdog.
Assistant Commissioner Brett McFadden said investigators would consider the domestic and family violence context and the history of the two people.
"It is a complicated set of circumstances involving two people, a man and a woman," he told reporters in Sydney.
"It's an absolutely tragic set of circumstances."
An active apprehended domestic violence order was in place to protect the woman, the senior police officer confirmed.
The order did not prevent contact between the two parties but did enforce several conditions on the man's conduct, including that he was not to visit the apartment premises, nor become intoxicated.
Paramedics assessed the 46-year-old woman for shock and minor injuries.
It was not yet clear if she obtained the minor injuries on Friday evening or if they were pre-existing, police said.
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