Police are searching for Nathan Te Hana in relation to the death of a 57-year-old in Linwood, Christchurch over the weekend.
On 3 January, emergency services arrived at an England Street property to help Michael Joseph Graham, but he died at the scene.
Police believe he was involved in an assault.
Police say they would like to speak to Nathan Te Hana as part of the ongoing investigation.
Te Hana, 46, is believed to be in the Christchurch area.
People with information which can help locate him can call police on 111, quoting file number 210103/2420, or anonymously via Crimestoppers on 0800 555 111.