Judge McGuire said the summary would be available at sentencing.
"For the benefit of the victim's family it is important that the circumstances surrounding this offending - what actually happened on that terrible day in January are accurate. Often that requires discussion between defence counsel and police so that the final summary is accurate."
In addition to requesting pre-sentence, victim impact and reparation reports, Judge McGuire directed that Curtis take part in a restorative justice process.
He said although there was no requirement for the victim's family to be involved, the court's experience was that it could assist the healing process.
Judge McGuire said legal mechanisms for dealing with tragedies of this nature were "limited and inadequate".
He said a reparation report would enable the defendant to "acknowledge and recognise the harm that had been done in a tangible way".
Counsel for Curtis, Richard Laurenson, said his client was keen to co-operate with any initiative that was suggested by the court.
The parents, family members and supporters of Genevieve and Curtis were in court for today's hearing.
In a statement released to the media Guy and Rose Lewis said Genevieve would have celebrated her 10th birthday last week but instead had lost her chance at life and they were missing her immensely.
They said they were keen to see a conclusion to the legal process.
"There are no words to describe the huge gap she has left in our lives and the lives of her brother, wider family and friends," the statement said.
Judge McGuire said he appreciated that Genevieve's family had travelled some distance to be at the court hearing in Taupo.
"I am sorry I can't wave a magic wand and make it all happen and complete it today."
Following the court hearing, Curtis' family members said he remained "absolutely devastated" by the tragedy.
The maximum penalty for the charge is a $10,000 fine or 12 months' imprisonment.
- NZPA