Allan Schoenborn stabbed his daughter and then smothered his sons at their Merritt home in April 2008, leaving their bodies to be found by their mother.
A resolution passed by city council Tuesday said the owners have until March 15 to destroy and remove the home.
Neither the mayor nor the chief administrative officer responded to emailed requests for an interview Thursday evening, but Coun. Kurt Christopherson said the issue was on council's radar for some time and also raised the question "who would live there?"
"It was very difficult on the neighbourhood to continue to have a reminder of a terrible tragedy that happened in the town," he said.
The resolution passed by council said the home was uninhabitable and abandoned and the city has received many complaints about its dilapidated condition since 2012.
The city unsuccessfully tried over the past few years to have the owners remedy the situation, it added, before declaring the property a "nuisance" under the Community Charter.
If the owners do not meet the deadline, the city can demolish the home and recover its costs by charging taxes against the property, said the resolution.
Schoenborn was found not criminally responsible for the deaths, has spent the subsequent years at a Metro Vancouver forensic hospital, and was denied escorted absences in February 2014.
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