He has links to Rotorua and Gisborne and is believed to know people in Hawke's Bay.
The incident was reported to police about 1am Friday after the woman was taken to The Rose Irish Pub in the central city by a man who came across her in a distressed state nearby.
She was wet, had no footwear and facial injuries.
Mr Crowe praised the intervention of the man, who had seen something happening and gone to check it out.
"He could see something was not right and he stepped in - he did a hell of a good thing."
Mr Crowe said it appeared there had been an initial incident on the beachfront - "but then it's continued back in town".
The man who assisted the woman and took her to the bar to seek help had come forward and had spoken to police.
Manager of The Rose, Vanessa Zietsman, said staff had been contacted by a person in the accommodation business alerting them there may be a man somewhere in the city centre who had been to a backpackers establishment, asking for a particular woman. It seemed the woman had been trying to avoid the man - although bar staff and police were unable to say whether it was linked to the attack.
Mr Crowe said there were no indications as to whether the man was still in the region.
