In a statement released through his lawyer Tony Ellis last night, Smith, 40, alleged a prison officer assisted in helping him obtain a passport and gave him a smartphone and movies.
Smith alleged he received "numerous benefits" from the officer from the time of their first meeting to sometime between October and November 2012.
Corrections Association president Beven Hanlon told Radio New Zealand today that Smith's claims relied on his credibility and were unsubstantiated.
"What we are saying is put up or shut up really.
"If he has got a corrupt Corrections officer, as he claims, nobody wants to be working with that person -- put up the evidence let's get it done and let's bunk them together if they're such good friends."
Mr Hanlon said the fact Smith claimed he had details of this prison officer proved nothing.
"Unfortunately it is not uncommon for prisoners to get the details of a Corrections officer, it's not hard. Details of a Corrections officer prove nothing.
"We get allegations made by prisoners with those sorts of details all the time."
Mr Hanlon said he believed Smith released the statement to get himself into the media.
"He is doing that successfully because it is a fantastic story to put out there. That is why we are saying put up or shut up.
"We haven't heard anything yet that actually substantiates anything he said," Mr Hanlon said.
Smith's lawyer Tony Ellis told Radio New Zealand that Smith paid the prison officer $7000 for his services.
"The method of payment... the details of that are unknown to me but I am reasonably certain that it could be substantiated."
Dr Ellis said he hoped the police would now speak to Smith so arrangements could be made for him to disclose the name of the prison officer.
Dr Ellis said he believed the person was still a prison officer, and Smith was confident he could identify him.
"He has a level of information that in my opinion would calibrate what he is saying, he has got sufficient personal detail.
"There are enough details about the officer that would identify him without any difficulty."
Smith was arrested at a Rio de Janeiro hostel last month, after fleeing New Zealand while on a 72-hour limited release from Spring Hill Prison.
Corrections northern regional commissioner Jeanette Burns said the allegations made by Smith were unsubstantiated and incomplete and had been referred to the police.
"The allegations may turn out to be serious but until they're properly investigated and tested in court they remain just that, allegations," Ms Burns said.
"They can form part of the ongoing investigation into his departure from New Zealand during a temporary release while under the supervision of his sponsor.
"These claims could also have an impact on the current court case in which he is facing charges."
Ms Burns said she was unable to make any further comment while inquiries were underway.
"While this prisoner faces charges and an ongoing investigation into his actions Corrections is unable to comment until the legal process has run its course and the ministerial inquiry is completed," she said.
- NZME.