She said the woman made three attempts to jump into the water, the first time after she fumbled onto a barrier.
"I thought oh, she's acting a bit odd. She put her handbag down and you can see she would not be able to sit up there. She would've fallen straight into the water and probably hit her head a few times going down."
Ms Anderson asked the woman if she needed any help.
"She'd had a bit to drink but she seemed quite disoriented, and when I looked closer I would say she even looked a bit depressed. Then she started to get a bit pushy."
Ms Anderson said the woman was determined to jump.
"She wanted to get into the water and I think it was a perfect opportunity to make it look like an accident."
Ms Anderson called over Wendy Forrest, a volunteer collecting donations for the Wellington Free Ambulance.
Ms Forrest fetched a paramedic and a police officer, who escorted the woman away.
The woman returned and Ms Forrest had to pull her back and send her away again.
"When she came back the second time, my mouth dropped open. I thought how could they have let her go," Ms Anderson said.
Ten minutes later the woman returned again and tried to get over the barrier.
Ms Forrest notified a second police officer, who Ms Anderson said was "quite abrupt".
The woman was clearly a danger to herself and police didn't take the incidents seriously enough, she said.
Ms Forrest has laid a complaint with the IPCA, prompted by the "slack" general attitude of the officers.
"I would have thought they would have seen the state she was in and smelt the alcohol, that sort of thing, and for her own safety taken her away."
She told the second officer the woman was a danger to herself, to which he replied he didn't know that.
"I said, 'you do now'. He was actually quite obnoxious and didn't give a stuff, and just ambled back to where his colleague was and that was the last we saw of them," she said.
"It's really disappointing because that was a family environment. She needed help and this could have been avoided."
Ms Forrest said she had complained directly to Wellington police and was given the brush-off.
She said she did not have much respect for police and questioned why Mr Ross was receiving a bravery award for doing his job, which his colleagues had put him up to.
Wellington police district acting professional standards manager Senior Sergeant Dave Rose confirmed a complaint to the IPCA had been received and would be investigated.
"No complaints have been made directly to Wellington police by any member of the public in relation to this incident," he said.
"Given this complaint is now subject to an investigation it's not appropriate for police to make any further comment until the investigation has concluded."