The police are not seeking the extradition of Alan Langdon, the 49-year-old man who took his six-year-old daughter to Australia in a small boat.
On Friday the police said they were investigating Mr Langdon, who they said had breached a family court order by taking the child out of New Zealand.
Que Langdon, who is the focus of a long-running custody dispute, was reunited with her mother, Ariane Wyler, in Australia yesterday.
Court proceedings were initiated yesterday under the Care of Children Act, and Mr Langdon is due in court on the 25 January.
A police spokesperson said there were no extradition proceedings in place and Mr Langdon would have to appear of his own volition.
A large search for Que and Mr Langdon was triggered after they left Kawhia on 17 December, apparently bound for the Bay of Islands.
Ms Wyler hired a private investigator to help find them.
Mr Langdon and his daughter were spotted in a coastal Australian township, Ulladulla, last week by a member of the public who alerted authorities.
Mr Langdon said last week that he had no plans to return to New Zealand.
Passport delaying mother and daughter's return - spokesman
Private investigator Col Chapman, who has been working for Ms Wyler, said she wanted to return to New Zealand but could not leave Australia because her daughter did not have a passport.
Ms Wyler would have to apply for the release of Que's passport, which was being held by the family court in New Zealand, he said.