Australian officials then refused the visa for extradition and the man has now escaped trial altogether.
In another case, Australian authorities decided the visa usually used for extradition cases was not needed because the man was eligible for a different visa.
He was sent to Australia where that visa was promptly cancelled and he was detained in an immigration detention centre, where he remains without having faced trial.
Little said there seemed to be a disconnect between state authorities and the Federal authorities who deal with the visas and immigration issues.
He had raised it with the Australian High Commission and was waiting for a response from the Australian government.
It risks becoming a further thorn in the relationship between New Zealand and Australia.
New Zealand is already concerned about Australia's immigration policy and Little said the new problem appeared to relate to changes to the Migration Act in late 2014 under which non-citizens are deported if sentenced to more than 12 months for crimes or if considered "a risk to the health, safety or good order of the Australian community".
Little described it as "changed immigration laws that sees them deporting New Zealanders on, I would say, flimsy grounds and now managing extraditees in ways they haven't been dealt with before".
There is a simplified process for extradition between New Zealand and Australia.
"There have been a number of cases involving New Zealanders that haven't followed the usual pattern that we would expect to follow for people extradited to Australia to face charges.
"There appears to be, as I would observe it, a mismatch between what state authorities are trying to do and the way Federal authorities are managing their immigration laws that apply to, in this case, alleged offenders who are facing criminal charges back in Australia," said Little.
"And we just need some clarity about what the rules are."
In a statement, a spokesperson from Australia's Department of Home Affairs said Australia "greatly appreciates" the assistance New Zealand provided.
"We want that co-operation to continue."
The statement did not directly address the issues in the cases Little was concerned about, but said since July 2017 no New Zealander extradited to Australia with a Criminal Justice Entry Visa had been removed prior to criminal proceedings ending.
The cases came to Little's attention when considering the case of a refugee in New Zealand who Australia wants to extradite to face charges over a people-smuggling venture which resulted in the deaths of 353 asylum seekers in 2001.
The Supreme Court last year ruled Little must personally decide whether to extradite Maythem Kamil Radhi, charged by Australia in 2010 for alleged involvement in offences relating to people smuggling.
Little said he was waiting for advice on that case and did not know how long a decision could take, but Radhi was entitled to know what conditions would apply to any extradition.
"To some extent it does relate to policies of the Australian Government and the way they are dealing with those who are extradited to Australia to face criminal charges, as well as the way they are managing deportations. We are awaiting clarification from the Australian Government on some critical issues that we need to resolve."
It could be a political headache for Little, whose options include refusing extradition - meaning Radhi escapes trial - extraditing him regardless of his fate, securing an assurance from Australia about Radhi's future or agreeing to a special visa to allow Radhi to return even if he was convicted for people smuggling.
Prime Minister Jacinda Ardern has described people smugglers as "parasites" and "repugnant people who are risking people's lives".
The Supreme Court referred the Radhi decision to Little, saying if Radhi was convicted and sentenced to jail it would leave him in "immigration limbo".
Radhi is an Iraqi refugee who has a residence visa but not citizenship in New Zealand. His wife and three children are citizens.
Radhi was accepted as a refugee in New Zealand in 2009 and Australia tracked him down and sought to extradite him in 2010.
The court said, if convicted, Radhi's New Zealand visa would lapse and Australia's policies would likely mean he was put into an immigration detention centre as soon as his sentence ended with nowhere to deport him to.
The court said a possible solution was for the Immigration Minister to grant Radhi a visa in advance that would allow him to return to New Zealand even if he was convicted and served time.
