New Police Commissioner Mike Bush says his public apology to Arthur Allan Thomas is enough and he won't be putting it in writing to the Thomas family.
Mr Bush was criticised after speaking at the funeral of former police officer Bruce Hutton last year and praising him as an officer whose integrity was beyond reproach.
A 1980 Royal Commission found Mr Hutton had planted evidence that led to the wrongful conviction of Mr Thomas for the murders of Harvey and Jeanette Crewe a decade earlier.
Mr Bush apologised in February for any offence his comments had caused anyone, and said that in hindsight the remarks were probably inappropriate.
Arthur Allan Thomas's brother, Des Thomas, told Radio New Zealand at the time that Mr Bush should say sorry in writing and address what he calls the police corruption in the Crewe murder case.
Mr Bush says, however, that he has already made a public apology and has nothing more to add.
He was inducted as the new commissioner on Thursday.