The woman was discovered at the Richmond Village Green on Stanmore Rd last Wednesday.
Police said the woman remained in hospital, but her condition was now stable and they had spoken to her.
Officers were continuing to work to establish the full picture of what happened, and who was responsible.
"While police do not believe there is an ongoing risk to the wider public, additional patrols have been operating in the area to ensure the community feels safe," a police spokesperson said.
"We are still appealing to anyone who may have information that would help us determine what happened."
Information can be passed to police via the 105 phone service, or by going online and using 'Update Report', referencing file number 250205/8067.
People who live near the park previously told RNZ day-drinkers, drug users and homeless people spent time there.
A woman, who did not wish to be named, said it was a "dodgy area" so she avoided the park.
"There's always people loitering around, I don't see many families go and play there apart from... I'd say like, druggies. There's always older people just standing around the park, I wouldn't say it's safe for kids. I don't usually go around walking."
