Clare Nowland was tasered during a confrontation with police while walking with a frame and holding a steak knife at the Yallambee Lodge in Cooma on May 17.
The mother of eight, who had dementia, died a week later in hospital.
A 71-word press release approved by Police Commissioner Karen Webb was issued 12 hours after Mrs Nowland was injured but provided scant detail about her "interaction with police".
"No further details are available at this time," it said.
Documents obtained by AAP under Freedom of Information laws reveal the statement was published after police slashed a much longer draft that included key details including the use of the Taser, the presence of paramedics and Mrs Nowland's possession of a knife.
"When she stood up and moved towards officers, a Taser was deployed by a constable," one of the lines in the 171-word draft prepared by the force's media unit said.
Police Minister Yasmin Catley told parliament on Tuesday she did not know about the more detailed draft until the opposition raised AAP's report in question time.
She said Ms Webb had been up front from early on about the reason for the brief press release, ensuring Mrs Nowland's large family could be informed.
After issuing the initial release, police did not make further statements until media reports emerged more than 36 hours after the tasering.
The minister's ignorance about the draft release was "extraordinary" and called into question her competence and fitness to remain in the job, Opposition leader Mark Speakman said.
"Of course, the police minister was not involved in the initial censoring," he said.
"But it's extraordinary that a police minister discovers this issue when it's reported in the press today and we asked about it.
"She should be proactive in seeking briefs."
Mr Minns rubbished those calls and said the public already knew about the circumstances of why all details weren't in the first media release.
"The release of the FoI didn't substantially change the circumstances related to the media release," he said.
"I don't believe it's substantial enough to remove the minister from her portfolio and I think reasonable people would (agree)."
He warned calls of a police cover-up could be misinterpreted as more than a communications strategy over a family's welfare.
"I would be concerned if there were any evidence that the initial police investigation into this death was compromised in any way," he said.
"The circumstances related to the original media release as described by the police commissioner are reasonable given the circumstances."
The draft noted the woman was treated by paramedics at the scene and left space for her latest hospital condition to be included.
The published statement omitted both details, stating her condition was "being monitored" in hospital.
The officer's job being placed under review was also removed.
Mrs Nowland was not named in both versions, as per standard police procedure.
Five days after the tasering, Ms Webb said the 36-hour time window was used to inform Mrs Nowland's family who deserved to learn about the incident via police, not the media.
Her comments that day did not reveal the omissions had extended beyond the mention of the taser.
NSW Police said the determination of the content and timing of information released to media on May 17 considered the extended Nowland family, the gravity of the situation and that the critical investigation team was not on the ground until that evening.
"Our priority was to ensure family members learned details of the incident directly from police rather than third parties and to ensure the integrity of the investigation," a spokeswoman said in a statement on Tuesday.
"The approach taken was consistent with NSW Police policies."
The officer who fired the stun weapon has since been suspended with pay and charged with three offences, including recklessly causing grievous bodily harm.
Senior Constable Kristian White, 33, will appear in a Cooma court on July 5.
