The statement, distributed via the Twitter handle @AerithXOR2, accuses the Ottawa police of laying charges at the behest of the FBI, without any proof.
The statement identified an Ottawa police detective. Media reports say the teen is alleged to have made fake emergency calls all over North America.
The Ottawa police website was inaccessible all morning following a weekend hacking incident loosely linked to the Internet group known as Anonymous.
Media reports say the group has targeted the police site, as well as the City of Ottawa's site, which was in inaccessible early Monday but back online by midday.
"When the police releases something, or makes claims, they better have 100 per cent proof to back up their claims," the statement said. "Otherwise, you can expect us coming."
The web problems follow an incident Friday when visitors to the city's website saw a dancing banana graphic and a brief text message directed against an officer with the city's police force.
Those responsible have also threatened to go after other government sites, including the Supreme Court and the Parliament of Canada, although both sites were still accessible at midday Monday.
The City of Ottawa says it doesn't believe any sensitive information has been compromised.
Police say they are continuing to work with their service providers "to address the service issues affecting ottawapolice.ca" but added they could not comment on the ongoing police investigation.
In a release Saturday, the city said it was "confident that no corporate or resident information was compromised as a result of the breach."
It said the "issues were related to a third-party service provider."