Rorotanga is part of the Cook Islands which are an independent, self-governing group of islands located in the South Pacific. It is the the largest island in the group, and the one on which the capital city is located.
It appears that, even though they are self-governing, the Cook Islands are a sub-division, or protectorate, of New Zealand – and have much the same relationship with New Zealand that Singapore and Hong Kong have with The Peoples Republic of China. From that association it can be deduced that since New Zealand has extradition treaties with the US, in all likelihood, the Cook Islands DO also.
I believe that the only restriction would be (like most British Commonwealth nations) they will not allow extradition back to the US to face a death penalty.