In 2012, the Manukau District Court found Radhi was eligible to be surrendered to Australia.
However, the decision was overturned at the High Court because Radhi's charges were not seen to have met the threshold for extradition.
Police then appealed against the High Court's decision at the Court of Appeal, which in July ordered the case to return to the District Court and ordered a warrant for Radhi's arrest.
In a judgement, delivered today, Supreme Court judges Justice John McGrath, Justice William Young and Justice Terence Arnold declined Radhi's application for leave to appeal.
"We do not consider that the interests of justice require that we hear and determine the proposed appeal."