FINTRAC is not an investigative body, so there is no overlap with law enforcement. It receives transaction reports, voluntary information reports, from law enforcement and sometimes from its international partners. It conducts analyses of the financial information. Where it has reasonable grounds to suspect that there's been either money laundering or terrorist financing, it turns this information over to the appropriate law enforcement agency. That's where the law enforcement agency takes over the investigation.
On October 31st, 2006. See this statement in context.