Police say the Kahui investigation will remain closed unless new information comes to light, despite the prime minister saying they should revisit the case.
Chris Kahui was on Thursday found not guilty of the murders of his three-month-old sons - Chris and Cru - in June 2006.
After the verdict, police said they believed they had arrested the right person and would not be charging anyone else over the boys' deaths.
"There is no evidence to support a charge against any other person and that includes the mother, Macsyna King," inquiry head Detective Inspector John Tims said.
Speaking at her post-cabinet press conference after the police had issued their statement about the case, Miss Clark said she had talked to Commissioner Howard Broad yesterday and he had explained it was standard practice to hold an extensive debrief.
"The jury dismissed the case so the police will debrief to see whether there are any other angles they should be pursuing,' she said.
"Under New Zealand's law of double jeopardy Mr Kahui cannot be tried again.
"So it would be a question of whether any evidence which comes to light points in the direction of any other person."
Miss Clark said proposed changes to the law of double jeopardy were in the Criminal Procedure Bill which has been in front of Parliament for more than a year.
One proposal was that when new and compelling evidence was produced which implicated an acquitted person, double jeopardy could be waived if the Court of Appeal was satisfied with the strength of the new evidence.
If that happened, the Solicitor-General could approve a new police investigation.
However, the legislation will not apply to anyone acquitted before it is passed by Parliament.
Miss Clark said she did not think "anyone of good conscience" could sit on information which hid the offender.
"Someone badly attacked those little babies which led directly to their deaths and that person should come forward, and those who know who it is should come forward," she said.
Counties Manukau district commander Superintendent Steve Shortland today reiterated Mr Tims' comments.
"Our decision, reinforced by advice from the Crown Solicitor, is that there is no evidence that would warrant re-opening the investigation or charging anyone else in relation to the death of the twins, at this point."
However, Mr Shortland said the case would be re-investigated if new information come to light. Mr Tims had earlier said the defence brought no new evidence to the trial.
Speaking on TV One's Breakfast show this morning, Prime Minister Helen Clark said someone needed "to be brought to account".
"The police are left thinking what do we do now? And while I understand in human terms the officer in charge of the investigation saying; 'that's it we've got nowhere else to go', I think you'll find that the police will sit down, they'll look at this, they'll sift back through the evidence they'll see whether there's any other angles."
She would not be drawn into criticising how police handled the case and the cultural sensitivity shown.
"It was an incredibly difficult investigation for them because a veil of silence came down over the entire family and everyone who knew them."
In another interview, on Newstalk ZB, Helen Clark criticised the children's mother Macsyna King.
Helen Clark said since the case became public she was concerned by reports the babies were not visited in hospital.
"Clearly there was a maternal love deficit of a gross kind. Very little interest shown in those very, very vulnerable small babies."
She repeated her view that police would look at the case again "in the cool light of day" and "and see whether there's new angles to explore".
However, it would be hard for police unless "someone could come forward with evidence a jury would find more compelling".
"I certainly would urge them (police) not to leave it where it is because our society now has in front of it a case where two beautiful young babies were killed and we don't know who did so justice has not been done."
Call for inquiry
Defence lawyer Barry Hart this morning called for an inquiry into the investigations of both the Kahui case and that of George Gwaze, who was last week cleared of the sexual violation and murder of his niece.
Mr Hart said he agreed with both verdicts but that large sums of money were spent by the Crown in both cases and that there were problems with the police investigations.
He said if charges were to be laid in the Kahui case they should have been against more than just Chris Kahui, whose lawyers argued the twins' mother Macsyna King could have been the killer.
Mr Hart said it was important that an independent body looked at whether the investigations was carried out properly.
However, Police Association vice-president Stuart Mills disagreed there were structural issues about the way prosecutions were brought and said there was no need for an inquiry.
"The public has to remember that in our current judicial system, acquittals do occur. In the case of Mr Kahui no applications to dismiss the charges were ever made," he told Radio New Zealand.
"The police are doing a very good job in trying circumstances. We need to make sure witnesses are co-operative with police as opposed to hiding at times family members who have committed a crime."
He said police had not decided to charge people for the sake of it and defended the time it took to make an arrest.
"Mr Hart says there was a long delay in the Kahui case. There was so they could actually assess all the information, but also the fact that the family were uncooperative throughout the investigation," he said.
- NZPA with NZHERALD STAFF