Jesse Leigh Green, 30, is accused of murdering 22-year-old Teah Rose Luckwell in the early hours of March 28, 2018, and his hearing continued in the NSW Supreme Court on Thursday.

Detective Sergeant Scott Craddock gave evidence in the case before he was cross-examined by public defender Stuart Bouveng.

Mr Bouveng asked the witness about a number of men police considered to be people "of interest" in early investigations, before Green was charged.

Detective Sergeant Craddock told the court one particular man was a person of interest because he was believed to be the last person to see Ms Luckwell before she was killed.

Mr Bouveng said the man was "effectively home alone" that night and had told police he was gaming on a PlayStation.

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The public defender suggested no one had attempted to clarify that until June 2019, more than a year later, which Detective Sergeant Craddock accepted.

Mr Bouveng said the "lapse of time" between the murder and police contacting the internet provider meant no specific data details could be provided other than that there was a connection to the address.

"That's an accurate representation," Detective Sergeant Craddock replied.

The court heard there had not been a search warrant executed at the man's home.

No one besides Green has been charged in connection to the alleged murder.

Mr Bouveng asked about evidence given earlier in the hearing that a local family believed they had seen Ms Luckwell late in the morning on March 28 at Kmart in Tamworth.

Detective Sergeant Craddock said he had watched the available CCTV content from that day and the day before.

The court heard that although police were aware Ms Luckwell was known to use public transport to get around town, no footage had been requested from bus lines for March 28.

The Crown case is that Green stabbed Ms Luckwell in the neck and back inside the front door of her social housing unit on Robert Street in the early hours of March 28 before fleeing. Her body was found that night. Further witness statements were also read in court on Thursday.

"That substantially completes the evidence in the Crown case," prosecutor Brian Costello said. Green faces charges of murder, break and enter, and using an offensive weapon.

The hearing is in its fifth week and continues before Justice Stephen Campbell.

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