Mark Tedeschi was expected to make oral submissions on behalf of NSW Police to the special inquiry into LGBTIQ hate crimes in Sydney on Friday, to examine ways police have approached "bias crime" from 1970.
The matter was first heard over several weeks in December with evidence from three police strike forces - Macnamir, Parrabell and Neiwand.
Macnamir centred on the death of American mathematician Scott Johnson in 1989 at a Sydney gay beat, for which Scott Phillip White was jailed three weeks ago for nine years after admitting to manslaughter.
But Mr Tedeschi on Friday instead argued evidence regarding Macnamir was irrelevant to the inquiry.
Any material regarding former NSW Police deputy commissioner Michael Willing and detective Pamela Young, who were both involved in the investigation, was also argued to be irrelevant.
The inquiry is expected to return on Monday after both parties resolve the issue.
During the December hearings, police also took issue with the relevance of some material before the inquiry and the resources needed for the probe.
A letter claimed the inquiry's orders meant about a dozen investigations and reviews by the unsolved homicide team had been delayed.
The inquiry's commissioner, Justice John Sackar, at the time dismissed the claim as a "misguided and misconceived" assertion and "offensive" to the special inquiry.
The inquiry into LGBTQI hate crimes has been examining the unsolved deaths of 88 gay men between 1970 and 2010.
The 13th and final block of hearings will occur next week, and Justice Sackar will deliver a final report in August.
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