Detective Inspector Mark Loper of Bay of Plenty police said the case has been reviewed periodically over the past 32 years, with the file coming to his desk earlier this year.
"Mr Tahu left behind a wife and two children who have had to grow up without a father. For the past 32 years they have had to grapple with the unresolved circumstances of his death and it's as important for them as it is for us to be able to make this arrest and put the case before the courts.
"We will always do our very best for victims of crime, regardless of the age of the case.''
Mr Loper said Mr Tahu's family had expressed their thanks and relief at the latest developments but asked media to respect their privacy.
Rodney Tahu, 32, was shot in the head at Turangi Service Station shortly after 1am on Thursday 16 August, 1979. He was taken to Te Awamutu Hospital but he died shortly afterwards.
Mr Loper of Bay of Plenty police said the case has been reviewed periodically over the past 32 years, with the file coming to his desk earlier this year.
Bay of Plenty Police district crime manager Tim Anderson said the Tahu family - a widow and two sons now aged 40 and 42 - were "very happy'' an arrest had been made.
"But this just the first step,'' Mr Anderson said.
"[His children] have had to grow up without a father and for the last 32 years they have had to grapple with the unresolved circumstances of his death.''
