The 21-year-old died in the early hours of March 18, 2012, after being chased by 11 police officers who repeatedly tasered him.
Mr Curti had stolen a packet of biscuits from a convenience store and was delusional and behaving erratically after taking a small amount of LSD.
Senior Constable Chin Aun (Eric) Lim, Senior Constable Damien Ralph, Senior Constable Scott Edmondson and Constable Daniel Barling stand accused of assault.
But defence lawyer Brett Walker SC said the evidence from direct interviews taken should not be admissible.
The defence has argued that during the interviews, officers were "compelled" to answer questions by threat of disciplinary action and therefore their answers should not have been used against them.
Instead, Mr Walker argued, the interviews became "inextricably entangled" in the ensuing investigation of them.
This meant the prosecution case was "rooted in an eradicable error," he said.
"We challenge the prosecution to say there's any charge based on other material," he said.
But Crown Advocate Natalie Adams SC, appearing for the attorney-general, said only three pages of Lim's interview had ever been handed to the DPP.
If the admissibility of the interviews was in question, Ms Adams said there should be an application for that evidence to be excluded under section 138 of the Evidence Act.
"This is not a basis for a stay," she said, adding that should be a "last resort".
New South Wales coroner Mary Jerram had, in 2012, made scathing findings against the police officers present on the night of Mr Curti's death, describing them as "thuggish".
Magistrate Mark Buscombe will rule on the application for a stay of proceedings on November 11.
