The Crown can appeal a finding of Not Criminally Responsible but only in very limited circumstances. The Crown has to show the trial judge made a material legal error in charging the jury, the jury's verdict was perverse or somehow the decision was a miscarriage of justice. It is not enough that the decision was wrong - the jury are entitled to be wrong just so long as they are not perverse.
And that means an appeal in the Kachkar case would likely fail. The trial judge appears to have given a perfectly acceptable charge. Kachkar's behaviour, screaming about Chinese technology and the Taliban, as he ran in a snowstorm barefoot from the Good Shepherd homeless shelter stealing an idling snowplow from in front of a Regent Park Tim Hortons and taking it on a demented joyride, is weird enough to justify an NCR finding. And remember a psychiatrist hired by the Crown testified for the defence!
The Criminal Code provides: