A 13-year-old boy had been remanded to a secure Child, Youth and Family centre after police arrested him as a suspect in the killing of a caregiver near the remote settlement of Urenui, north of New Plymouth on Sunday.

The young man appeared in court in New Plymouth on Monday, as police have yet to piece together the results of their investigation.

Rose Kurth, a 50-year-old caregiver, was found dead by her partner in their home. She died almost instantly from a gunshot wound to the head. A neighbor who had come to help thought she heard something in Ms Kurth's house, but that it was nothing serious.

A firearm was recovered at the scene of the crime, but police are not disclosing any more information.

The young suspect was stopped by police near the scene of the crime, and police are still appealing for anyone who saw a four-door white 1993 Ford Telstar car driving near the crime scene and stopped by police in Waitara to come forward and help in the investigation.

Police had later found from Ms Kurth's neighbor that the suspect was taken in by Ms Kurth and her partner, and he seemed to be a decent young man.

Detective Senior Sergeant Grant Coward of New Plymouth CIB told New Zealand Herald the boy had been remanded to a secure Child, Youth and Family centre until Friday.

"We are very interested in hearing from people who saw that car on the roads between Okoki and Waitara, between 3.30pm and 5pm,'' Detective Coward said.