Hearing police sirens approaching his Forest Lodge home, murder accused Blake Davis allegedly said "F***, I'm going to jail", according to police facts tendered in court.

Police say the 28-year-old had just struck rapper Jett McKee in the head with a samurai sword after the hip-hop artist fled following a botched home invasion.

Mr Davis and his girlfriend Hannah Quinn, 23, are charged with the murder of McKee, also known as Scepaz.

Key points: Hannah Quinn and her boyfriend turned themselves in to police after three days on the run

Hannah Quinn and her boyfriend turned themselves in to police after three days on the run The court heard Quinn did not know what her boyfriend was going to do

The court heard Quinn did not know what her boyfriend was going to do The surety for Ms Quinn's bail was $60,000

Ms Quinn broke down in tears from Silverwater Jail when she was granted bail at Newtown Local Court via videolink on Thursday.

A police statement of facts tendered during her bail application reveals graphic detail of the alleged moments leading up to and following McKee's death.

Police allege Ms Quinn and Mr Davis were home shortly before 1:00pm on Friday when McKee entered their granny flat with a balaclava, replica pistol, pepper spray and knuckle dusters, and demanded money.

Mr Davis told him: "There's no money here," before McKee punched him in the face with the knuckle dusters, police allege.

Ms Quinn told police she chased McKee from the home after he took off with her bag.

Police allege she gave chase down Hereford Street, screaming "Who are you? Who the f*** are you?" and Mr Davis, allegedly armed with a samurai sword, followed about 10 metres behind her.

When she caught up to him, Ms Quinn allegedly grabbed his jacket and flung him to the ground.

Hip-hop artist Jett McKee, known as Scepaz, was found dead on a Sydney street on Friday. ( Supplied )

As he was kneeling on his hands and knees Mr Davis "swung the samurai sword downwards with force impacting heavily with the deceased's skull causing a large open wound and bleeding", according to the police case against the pair.

"What the f*** have you done?" Ms Quinn said.

The wound to McKee's head was 25 centimetres long and police examining the road discovered "a large pool of blood mixed with body and brain tissue", the police fact sheet said.

Police allege Mr Davis armed himself with the samurai sword, causing McKee to abandon the home invasion as the pair gave chase.

"It is the police case that accused Quinn knew accused Davis would strike the deceased with the samurai sword if he was able to catch him, causing grievous bodily harm or death," the document said.

Following the incident, the pair allegedly hid in a nearby laneway, in which a paper bag containing more than $21,000, two mobile phones, six numb chucks and a pistol, believed to be a pellet gun, was found.

Police said Strike Force Hedda had been established to investigate the incident and could charge the two with further offences, including the unlawful possession of the contents of the paper bag.

During Ms Quinn's bail application, her defence barrister Tom Hughes said she did not know what her boyfriend was going to do and that she "was a 23-year-old girl, with no criminal history and was subject to a particularly unpleasant home invasion", which left her "traumatised, terrified and in a state of shock".

Hannah Quinn had been in prison since the weekend. ( Supplied )

Mr Hughes argued McKee threatened the couple, saying: "You don't want to get hurt, I will shoot you — there are a lot of people like me who will shoot you — give me your valuables."

The court also heard McKee had a large gambling debt, which had been paid off by his parents, and a girlfriend who was pregnant.

Police prosecutor Clint Nasr did not oppose Ms Quinn's bail application, but will be pushing for the murder charge to remain, as well as an additional charge of being an accessory after the fact.

After three days on the run, the alleged killers turned themselves into Newtown Police Station on Monday night, where they were both charged with murder.

In granting bail, Magistrate Margaret Quinn said she was satisfied that the TAFE student did not "pose an unacceptable risk" considering "she had no previous criminal record" and was subject to "an unfortunate incident".

Outside the court, the accused's mother Megan Quinn thanked people "for keeping an open mind" and expressed her sympathy to McKee's family.

Mr Davis and Ms Quinn are due to face court again in October.