A 12-year-old living in state care who said she was raped three times faced "pointless and repetitive" questions from police, a Family Court judge says.
In his ruling, Judge Alex Twaddle also said the investigation into the complaints, which were made nearly a year ago, had taken too long and officers needed to try harder to solve them.
"Serious allegations have been made and they need to be followed up with much more determination," he said.
The girl has declined to give a second police interview.
Judge Twaddle also said the ministry's supervision at the home where she was living "was completely inadequate".
The Ministry for Vulnerable Children said in a statement the allegations were the subject of a current police investigation and that process should be allowed to proceed.
"We are looking at how we can better cater for the needs of this group in the future design of our family homes."
It said it was challenging finding the right placement for every young person in its care.
The girl first told her mother about the abuse in September 2016. She said the rapes took place when she ran away from a state-run home in the Wellington region, where she was in the custody of Child Youth and Family, now called the Ministry for Vulnerable Children.
In an interview with police six weeks later, in November, she accused three teenage boys, two aged 14 and one aged 16.
The mother's lawyer called the hour-long interview of the girl "torture", and the girl's lawyer said it was "abusive" and should have stopped sooner.
Judge Twaddle noted how the girl spoke "in considerable detail about absconding from the home, drinking alcohol and being forced to have sex on three occasions", twice on separate occasions in August, and once probably in mid-September 2016.
The judge said the police interviewer, a woman, went on asking questions about aspects of the girl's evidence "well beyond what was necessary; some of the questions were pointless and repetitive".
The girl "reached a stage where she was irritated and writhed uncomfortably in her chair, saying she could not say more," he said.
A social worker told the court they sent the girl back to the same home, even after learning of her rape complaints, because there was nowhere else to place her.
The social worker was unclear on when she learned who the accused boys were and whether one of them was living in the same home as the girl at the time.
The girl was repeatedly returned to that home after claiming being abused. The police said that their report listing the names of the accused boys went to the ministry, followed by an email "re-affirming police's concern and again listing the boys’ details".
The lawyer for the child told the court he had asked for a copy of the video interview in April, got no response and did not get a copy until August, which was "extremely frustrating".
The girl has so far declined another interview, stalling the investigation, while her mother has not responded to two invitations to give police a statement.
The judge said the situation was not straightforward because of difficulties in getting more information, but expressed his concern at how long police were taking.
He criticised the mother as self-centred for declining to make a statement to the police.
The girl ran away more than 20 times from the state-run home - on one occasion she was out from about 2am to 6am. The ministry said her mother encouraged her to run away.
The judge said different arrangements for her should have been made much earlier.
In a statement, police said allegations of rape were followed up with priority and diligence.
"This matter is particularly complex and is taking some time for a range of reasons."
As for the video interview, police said Judge Twaddle's comments were noted.
They said interviews were conducted by trained specialists and they tried to follow best practice.
"Interviews of [cases of] a sexual nature can be distressing for the victim. We aim to put victims at the centre of our focus and support them through this process. Police need to ask a range of questions to establish the full circumstances of an offence to build a case."
Police said they would have the interview peer reviewed.