Guy Turcotte was granted bail last September while awaiting his first-degree murder trial, which is scheduled to begin in the fall.
In December, the Quebec Court of Appeal affirmed a lower court's ruling that Turcotte was not a danger to society and could remain out on bail without undermining the public's faith in the judicial system.
The Crown, who'd sought to have Turcotte's bail revoked, said in a terse statement it would not seek to appeal that decision to the Supreme Court of Canada.
It did not give any reasons for its decision, but time would have been tight as Turcotte's second trial is scheduled to begin in September.
Turcotte was found not criminally responsible in 2011 in the fatal stabbings of his two children, Olivier, 5, and Anne-Sophie, 3.
He briefly spent some time in a mental hospital before being released.
The original verdict was overturned by the appellate court in 2013 and a new trial was ordered.
Turcotte is free on several strict bail conditions.
In granting Turcotte bail, Quebec Superior Court Justice Andre Vincent said that a reasonably informed public wouldn't be shocked by the decision.