Security camera footage from a nail salon less than 200 metres from the crash site shows the Volkswagen Tiguan patrol car travelling at speed down Gibbons Street in Redfern, with sirens and lights blaring, before the fatal accident about 1.30am on Friday.
The officers were responding to a reported vehicle theft in nearby Glebe.
Lay's father, Clem Lay, told the Herald that after his initial anger, he was relieved that Torrisi, his daughter's fellow officer, had survived the crash. "I want [Mia] to be remembered by as many as possible for as long as possible," he said. "Everyone that she touched in her life has paid tribute."
He told Nine News he hoped there was "no one at fault" for the crash, saying that the immense loss his family is experiencing still had not hit home.
Mourners have filled the crash site with flowers and tributes to Lay. Former colleagues and schoolmates were among those who left written tributes. One mourner tied a NSW Police badge to the tree with a scarf bearing the colours of the police uniform, while others brought shirts bearing the insignia of APIA Leichhardt, Lay's former football club.