NSW police have charged Mert Ney, 20, with murder following a brutal attack in Sydney's CBD.

Detectives said Ney has been charged with murder, attempted murder, wounding a person with intent to cause grievous bodily harm, intentionally choking a person with recklessness, and common assault.

He has been refused bail to appear at Parramatta Bail Court tomorrow, news.com au reports.

Mert Ney, 20, allegedly killed Michaela Dunn, 24, in a Clarence Street apartment on Tuesday before allegedly stabbing Linda Bo, 41, in the shoulder at the Hotel CBD.

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He was later filmed running through the city streets brandishing a knife before being restrained by onlookers and arrested.

Ney was taken to Royal Prince Alfred Hospital for treatment but was released and transferred to Surry Hills Police Station for questioning just after midday on Friday.

Investigators have been trying to piece together why Ney — who had a history of mental illness — allegedly launched the attack.

NSW health authorities are reviewing his care and treatment in the lead up to the alleged attacks.

The NSW opposition says it's concerned communication between departments broke down, following a News Corp Australia report that Ney was staying in government emergency housing while police were searching for him over a domestic violence incident.

Ney was allegedly carrying a USB stick with information about recent mass casualties in New Zealand and the United States and could be heard on video footage shouting "Allahu Akbar".

NSW Police have not classed the attack as a terrorist incident and have not identified any links to terrorist organisations.