He alleged with the officer's assistance he had the phone until December last year.
He also alleged the officer suggested he consider escaping.
"He also suggested that I could consider escaping to South America 'as many of the Nazis did following the Second World War'." "Those were his words," Smith said in his statement.
Smith was arrested at a Rio de Janeiro hostel, after fleeing New Zealand while on a 72 hour 'limited release' from Spring Hill Prison.
He alleged the officer provided him with a passport application, assisted with passport photos, then posted it once completed.
Watch: Smith's rude gesture as he leaves Brazil
Smith said he felt "failed" by this officer.
"At the time that I was approached by this corrupt government official I was trying to address my offending in a treatment unit.
"I feel that government officials should be role models and that this officer had a responsibility to report me for what contraband I had, and to give me good advice for my future.
"I was failed in this regard."
Smith said there was "much more to this story" and said he was happy to discuss the matter with the Police.
Corrections northern regional commissioner Jeanette Burns said the claims haven't been substantiated, but have been passed on to police to investigate.
A police spokesman said they would not be making any comment at this stage.
Smith caught on camera at Auckland Airport as he flees the country.
Timeline:
1974 - Born Phillip John Traynor
1992-95 - Sexually abused his neighbour's son in Carterton.
1995 - Murdered the father of the boy he was abusing while on bail for extortion, and escaping police custody while on bail for earlier offending.
April 15, 1996 - Sentenced to life, with a minimum non-parole period of 13 years, for murder, sexual offences against his victim's son, aggravated burglary of the family's home and kidnapping of the victim's wife and son.
April 14, 2009 - First time Smith is eligible for parole. Parole Board addresses multiple frauds committed in prison between 2006 and 2010. Investigation begins in to a business he was running behind bars and other fraudulent activity.
February 4, 2011 - Appears before Board again. The Board raises concerns about the "violent callous and manipulative aspects of his offending".
May 3, 2011 - Appears before the Parole Board, which orders a Parole postponement of two years.
April 8, 2013 - Parole postponement lifted and parole declined. Smith begins having 12 hour temporary releases.
March 31, 2014 - Smith is denied parole again. The Parole Board identified his risk of reoffending as high, and that if it were to occur it would likely be in the form of fraud. Board recommends further temporary releases.
Thursday, November 6 - Smith is collected from prison by an approved "sponsor", a family member. That same day he leaves the country using a passport in the name Phillip John Traynor and flies to Chile.
November 13 - Smith was caught at a hostel in Rio de Janeiro.
November 28 - Smith is deported from Brazil.
November 29 - Smith arrives back in New Zealand.
December 9 - Smith appears at Auckland District Court via audio visual link, charged with escaping lawful custody while allegedly on the run in South America and a charge of false representation was added to that in relation to how he obtained a passport.
Smith arrested outside a hostel in Brazil. Photo / AP
