Police Commissioner Howard Broad is considering whether to reinvestigate the Crewe murders after a personal plea from their only child.
He confirmed yesterday he had received a letter from Rochelle Crewe - 18 months old when her parents were killed - asking him to reopen the file.
She broke her silence yesterday for the first time in 40 years to say no-one had been held accountable for her parents' murders.
Comm Broad is yet to decide what action to take, but did not rule out a new investigation.
"It may be a very long shot to expect that any other sort of court action might flow from this," Comm Broad said.
"What's coming out is that there are a lot of unanswered questions about this case, and a lot of contested questions, and people are looking for answers.
"Whether or not it's possible to do that, I'm not sure."
When asked about Ms Crewe's quest for justice, he said: "That's the issue here. These are questions about a case that happened a long time ago and sometimes there is not satisfaction."
Police Association president Greg O'Connor said the case had been a black mark against police and it should be re-opened.
"When you consider that my generation of police officers have had that thrown in our faces continuously ... maybe a properly conducted inquiry wouldn't be a bad idea."
Prime Minister John Key said it was unlikely the Government would set up an independent investigation, but he did not rule it out.
He said a formal request would be needed to launch such an inquiry.
"We haven't seen any formal indications that that should or could happen.
"It obviously happened an awfully long time ago.
"I wouldn't want to rule that out, but I wouldn't have thought it's terribly likely.
"But given the length of time that's gone on, I would imagine it would be extremely difficult to do that.
"Not impossible, but difficult," he said.
Labour leader Phil Goff said the Government owed it to Rochelle Crewe to look at the evidence with a fresh eyes.
"The rest of us can only really imagine the difficulties she has gone through and the trauma, given the events surrounding her parents' death, and her really strong desire to have the truth known."
Others calling for the case to re-open include Peter Williams QC, defence lawyer of Arthur Allan Thomas, who was convicted of the Crewes' murders and spent almost 10 years in prison before being pardoned in 1979, and Crewe murder authors Pat Booth, Chris Birt and Ian Wishart.
The three writers have different theories as to what happened in what is New Zealand's most enduring murder mystery.
Jeannette Crewe's father, Len Demler, found "a terrible bloody mess" in the Crewes' farmhouse in Pukekawa, south of Auckland, in June 1970.
He also found his granddaughter, Rochelle, crying in her cot.
Doctors who examined her said she could not have been abandoned for five full days since the murders, so someone must have fed her.
Witnesses reported seeing a blonde woman at the house, but she was never identified.
The body of 30-year-old Jeannette Crewe was recovered from the Waikato River in August 1970, her jaw badly broken.
Her 28-year-old husband was found in the river a month later, weighed down by an axle.
Both had been shot.
