In their decision, they said: "The case raises no issue of principle and nothing put forward on behalf of Mr Dawood indicates a risk of a substantial miscarriage of justice."
Dawood pleaded guilty in April 2012 to the murder of his wife, Eman Hurmiz. It was the result of a culmination of a history of threats and violence towards her, depression and an abnormal jealousy over her imagined infidelity.
On September 2, 2011 Dawood lured his wife to a shed at the back of their Wellington property, tied her to a chair, took a large knife and began stabbing her.
Once his wife had died, Dawood attempted suicide, but was revived by emergency services.
He pleaded guilty to murder, aggravated wounding, assault, threatening to kill and possession of a weapon.