The seven men and five women have been considering their verdicts for more than an hour.
He earlier told the jury that the defendant's credibility was something they would have to put under the microscope.
Both Crown and defence gave their closing addresses yesterday and Justice Timothy Brewer is summing up the case in the High Court at Auckland this morning.
The defendant has been on trial for the last four weeks and denies the charges.
He opted to give evidence earlier this week and the Crown later said his whole case was a lie.
"[The defendant's] credibility is clearly an issue - you'll have to decide how credible he is," Justice Brewer said.
"The law says it's important for you to understand people tell lies for all sorts of reasons. If you do decide [the defendant] has told a lie you don't just write him off for that reason. You need to decide why he told the lie and put it into its appropriate context in the evidence."
The man charged with the murder of Blessie Gotingco. Photo / Sarah Ivey
The judge also said the trial had made it clear the accused had a criminal past, but that could not be a factor in the jury's consideration.
"You know he has some sort of criminal history. You have to put all that aside and all feelings aside . . . you are judges," he said.
"Your task is to decide what the Crown has proved, not to decide whether [the defendant] is a good person or a bad person and certainly not to jump to the conclusion that he has a criminal history and must therefore be guilty of these offences. It's a cold and unemotional examination of the evidence that's required."
The defendant previously told the court he was "smashed off his face" on methamphetamine on May 24, 2014 when the alleged murder took place.
But Justice Brewer said being high on drugs was no more an excuse than it was to be drunk.
However, he put the onus on the jury to decide how the drugs might have affected the man's mindset at the time and whether it explained his actions.
The judge was quick to point out that the Crown did not have to prove the killing was premeditated.
If they found the defendant hit her with his car by accident that did not mean he was not guilty, jurors just had to review what he did next, Justice Brewer said.
He also had advice for them when they reviewed the GPS evidence of the man's movements.
"Don't be fooled by the neat little yellow dots. Sure, sometimes they're accurate . . . but other times they're wildly inaccurate," he said.
Justice Brewer said he wanted unanimous verdicts and the jury had to be sure of the defendant's guilt if they were to convict him.
"As will now be totally clear to you, a trial is a time of testing. The onus of proof is on the Crown and the standard of proof required for proof of guilt is a very high one," he said.
