Then-senior constable Kristian James Samuel White, 35, fired his taser at Clare Nowland after being called to Yallambee Lodge nursing home at Cooma in southern NSW on May 17, 2023.
Mrs Nowland fell and did not regain consciousness and died in hospital a week later.
White was handed a two-year good behaviour bond and ordered to complete community service in March after a jury found him guilty of manslaughter.
Crown prosecutors quickly lodged an appeal against the "manifestly inadequate" sentence, which went before the Court of Criminal Appeal on Friday.
NSW Director of Public Prosecutions Sally Dowling SC argued Supreme Court Justice Ian Harrison made errors when he decided not to send White to prison.
One of the mistakes she alleged was the judge's finding that sending a strong warning to other police officers had only a minor role to play in sentencing.
"(Police) occupy a trusted role in our community and they must take the utmost care to use those weapons carefully," Ms Dowling said.
"This case required a sentence that sends a clear message that an unjustified resort to force or violence when other options are available will result in serious criminal punishment."
But White's lawyer Troy Edwards SC argued general deterrence had no role to play because his client made an error in judgment by believing Mrs Nowland posed a threat that justified the use of a taser.
He said it was "nonsense" to think a police officer who held a similarly honest but unreasonable belief would be deterred from deploying their taser as a consequence of White's sentence.
"If the officer has an honest belief that is unreasonable, general deterrence has no role to play," Mr Edwards said.
Ms Downing contested the suggestion White had an honest belief his actions were necessary.
She noted Mrs Nowland was experiencing dementia symptoms, relied on her walking frame to move and was "extremely vulnerable" when she encountered White.
During the brief, two-minute and 40-second encounter, White drew his weapon and pointed it at her for a minute before saying "Nah, bugger it" and discharging the weapon at her chest.
Mrs Nowland, who weighed less than 48kg, fell and suffered a fatal brain injury.
"(White) did not give her any real chance to avoid being tasered," Ms Dowling said.
"There were many other options available to him."
Mr Edwards criticised the prosecutor's argument Mrs Nowland posed "no threat", saying it flew in the face of evidence provided by those present at the aged care home.
He urged the three appeal judges not to intervene in the non-custodial sentence handed to White, which he said the crown had not proven was manifestly inadequate.
Ms Dowling contended it was "plainly unjust" that White escaped a jail term, which she maintained was the only appropriate sentence.
"The truly senseless, impatient and violent conduct of the offender requires a sentence that gives weight to denunciation," she said.
The panel of appeal judges will hand down their decision at a later date.
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