"Turiarangi now needs to do the right thing and hand himself into police."
Tiernan said anyone who may be assisting him to evade arrest could also face prosecution.
"We will be taking this type of behaviour very seriously," he said.
Turiarangi, 22, has nine warrants for his arrest for a number of charges including unlawfully taking a motor vehicle, dangerous driving, wilful damage and failing to stop for police.
Tiernan said these are not related to the homicide investigation.
"We have made a number of inquiries to locate Turiarangi but are now asking anyone who knows where he may be to please contact police immediately," he said.
"We believe that Turiarangi could be in the possession of a firearm and should not be approached.
If you know where he is then please call 111 immediately,."
Turiarangi has links across Auckland, Waikato and the Bay of Plenty.
Anyone with information that can assist the investigation team is asked to contact Detective Sergeant Brett Shields on 09 261 1300.