A Crown summary of the offending was read to the court, although Rizalman disputes aspects of it.
It says about 6.30pm on Friday May 9, 2014, Ms Billingsley was at her Wellington flat in Brooklyn.
"She was the only one home at the time and was watching a movie on her laptop in her bedroom," the summary says.
"Before entering the address, the defendant, Rizalman, removed his trousers and underwear."
He entered the flat through a closed but unlocked door.
In the kitchen, he took off his jacket.
Rizalman then knocked on Ms Billingsley's bedroom door and pushed it open.
"He spoke to the victim, saying, 'Can I come in?' The victim looked up from her bed and observed the defendant standing in the entranceway to the bedroom, wearing only a shirt and naked from the waist down," the summary says.
Ms Billingsley got up and began yelling and screaming for Rizalman to get out.
He approached her and grabbed her shoulders and the pair struggled.
Ms Billingsley managed to push Rizalman out of her room.
After removing him from the flat she locked the door and ran into the bathroom to call the police.
A neighbour heard screaming and called a flatmate, while a flatmate's boyfriend who lived nearby came to help.
He arrived to find Rizalman standing by the front door.
"By this time he had put his trousers back on," the summary says.
"The defendant was confronted, but eventually began walking away from the address on to the pathway."
Ms Billingsley suffered marks to her arms and "considerable emotional trauma".
Rizalman told police the pair had been to a cinema together. He claimed she invited him to her house but became angry when he ate her food.
Defence lawyer Donald Stevens, QC, said there was "no real dispute" about what happened in the house, apart from a suggestion by Ms Billingsley that Rizalman grabbed her throat.
Dr Stevens said Rizalman's hand might have come into contact with her throat, during a struggle.
He said he understood the Crown would dispute Rizalman was mentally unwell at the time, as the defence argues.
"Mr Rizalman has accepted there was an indecent assault because he went into the house without his trousers and underpants on, which made it indecent."
The assault itself was Rizalman grabbing Ms Billingsley's shoulders and arms.
Dr Stevens also asked Justice David Collins not to enter a conviction today, to which the judge agreed.
Crown prosecutor Grant Burston said the Crown didn't accept Ms Billingsley touched Rizalman first.
The most important thing was the "fear, slash, terror" she would have felt when Rizalman entered her house.
The Crown didn't agree with mitigating factors cited by the defence, Mr Burston said.
"It's not accepted by the Crown that the defendant followed the victim to her home because he thought the victim wanted him to follow her," he said.
"It's not accepted by the Crown that the fact the defendant removed his trousers and underpants prior to going into the victim's bedroom was not sexually motivated.
"Thirdly, it's not accepted by the Crown that the defendant was suffering from a significant mental illness at the time of the offending."
The defence would need to call evidence about that, Mr Burston said.
He said one expert's evidence suggested Rizalman's behaviour on the day in question was consistent with the use of cannabis and with anxiety.
Justice Collins bailed Rizalman until Friday, for a hearing about disputed facts.
MPs React
Green Party women's affairs spokeswoman Jan Logie said she believed Rizalman's guilty plea would be a "real relief" for Ms Billingsley.
She said the courts were "still not good places for [sexual assault] survivors".
"There is a lot of work that needs to be done to make them as fair and as comfortable a place for people to be able to seek justice," she said.
The Green MP was approached by Ms Billingsley last year. The victim was critical of the Government for letting her attacker leave the country and said that Prime Minister John Key appeared unconcerned with her case.
Ms Logie praised Ms Billingsley's bravery in waiving name suppression to speak out about her case.
"This is one of those situations where because she was brave enough to go public people were able to see the huge number of flaws in the process," she said.
The Green Party was now calling on Mr Key to apologise personally to Ms Billingsley on behalf of the Government.
Mr Key has previously said he would not apologise because former Ministry of Foreign Affairs head John Allen had already done so.
Ms Logie said a report into the Ministry of Foreign Affairs' handling of the case should also be released.
The report by John Whitehead was completed a year ago but would not be made public until Rizalman's trial was completed.
Foreign Affairs Minister Murray McCully said at the time that the findings in the report were "disappointing".
Labour's foreign affairs spokesman David Shearer said Rizalman's plea would make the court process much simpler for Ms Billingsley.
"Clearly, she had a very harrowing deal, now that we know the facts of the case," he said.
Mr Shearer said the full details of MFAT's handling of the matter should be released as soon as possible.
"The big question still remains why foreign affairs got this so wrong," he said. "And so far they have been hiding behind the John Whitehead report."
Acting Foreign Affairs Minister Todd McClay had no comment to make while the case remained before the court.
A spokeswoman said the Whitehead report would not be released until the court process - including any potential appeals - had been concluded.
