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Police say the naked woman found dumped in a layby was a 35-year-old mother of three teenage children.
A short time ago, police named the woman but admitted that the case was a difficult one as they have a gap of up to eight days in which they know nothing of her movements.
She was Rowena Kopara last seen on January 20.
Police Detective Inspector Peter Devoy told reporters that the woman had three children in their late teens and early 20s, who were in shock at her murder.
"She suffered a violent death," he said today but would not elaborate on the extent of her injuries.
She was last seen by relatives in Otara. Police say that no family members had reported her missing. Instead, police had identified her from their forensice examinations.
Mr Devoy said police are now trying to piece together any details of her movements and what she was wearing.
Ms Kopara's naked body was found at a layby near the Waikato town of Morrinsville late on Sunday night.
The body was badly decomposed.
No personal items were found and until today police were saying they had no idea of her identity.
The inquiry was upgraded yesterday to a homicide inquiry when police confirmed she had been murdered.
Police divers have been searching the Piako River in the hunt for clues to the death.
Police said the water was murky and it was not known how long the search would take.
The layby is used by motorists for a rest but is also something of a dumping ground for rubbish. Police teams are sifting through the rubbish for clues.