Senior Sergeant John van den Heuvel confirmed the woman had died after falling from the Internal Affairs building, but it was not yet known how many floors she had fallen.
"We're currently investigating the reasons and cause behind that."
Shopper Andy Dawson was walking along Lambton Quay with his wife and young son when he heard a "loud bang" about 15m away.
"It sounded like a small explosion at first. We saw people scattering around the sculpture, looking back in that direction, then looking up to see what it was.
"Then I just saw the lady lying on the curb... I thought she'd been hit by a car at first."
The woman landed just metres in front of a boy, he said.
"She just fell out of the sky, just dropped down in front of him."
Brandon Walker was crossing the road when he heard a thud and saw the woman lying on the ground.
"I rushed up to feel for her pulse, I couldn't feel a pulse. I stayed to see if I could find a pulse, couldn't find one. Then I just tidied her clothing and waited for the services to turn up."
Police were still working to establish who the woman was and were talking to witnesses on the scene, Mr van den Heuvel said.
"That will also give us the ability to offer victim support to those who have witnessed what's happened.
"We've got some very traumatised members of the public who have seen the lady fall or at least hit the ground."
Police were speaking to customers who had been at Gloria Jeans, which was now closed.
Parts of Lambton Quay and Waring Taylor St remain cordoned off.
