MPs have asked officials for more detail on how an information-sharing treaty with the United States would operate.
Representatives from the Police, Customs, and three ministries have appeared before the Foreign Affairs select committee.
The treaty has already been signed, but doesn't come into force until it is ratified by Parliament.
Under the agreement, the two countries could exchange fingerprints, DNA and other personal information related to serious crime - particularly terrorism.
Labour Party MP Phil Goff wants an assurance that information would be provided to the US only for fit and proper purposes.
Chair of the select committee John Hayes has asked how the information would be handled if the crime's punishment was the death penalty.
The officials told the committee they will provide more information before it meets again next week.