Aaron Ellmers was one of 399 deportees from Australia over the past five years.
They include sex offenders and other violent criminals who could not be subject to parole or other conditions as Corrections cannot enforce sentences imposed by foreign courts.
Police do not keep figures on the number of deportees returning to New Zealand having served a prison sentence abroad.
The national co-ordinator of Interpol in New Zealand, Detective Senior Sergeant Steve Dunn, said cases were dealt with "on an individual basis in response to information provided by overseas law enforcement agencies".
Any response by New Zealand police was dependent on receiving appropriate notification from those authorities. If notification was received, police would seek further information and carry out a risk assessment, Mr Dunn said.
Figures from the Australian Department of Immigration and Citizenship show that 399 New Zealanders had been sent home for failing a character test since July 2007.
A department spokesman said it was not possible to say how many of these had been deported after serving part of a prison term, as Aaron Ellmers did, but the number includes all deportees who have spent at least a year in prison.
In the 2011-12 year, 100 people were deported. When New Zealand deports sex offenders to Australia or Britain, those countries enter them automatically on sex-offender registers, meaning conditions such as supervision or mandatory reporting can be imposed.
Police Minister Anne Tolley is proposing a similar register in New Zealand, which would not be available to the public.
Sensible Sentencing Trust leader Garth McVicar backed the proposal but said it needed to be publicly available.
"Naming and outing these guys is the best form of rehabilitation available, in our opinion."
New Zealanders deported from Australia for failing a character test (including anyone sentenced to more than 12 months in jail):
July 2012-Dec 2012: 50
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