The objective of the Canadian TSB is to analyze the evidence and come up with findings. They are well known and well respected within the accident investigation community and there is frequently significant cooperation between the NTSB and the Canadian TSB.
Any time a Canadian registered, designed or manufactured aircraft goes down in the USA it will be the Canadian TSB involved in the investigation. The converse is also true within Canada. I think if you look up annex 13 you'll find a complete section of the Chicago Convention that deals with this.
There really are no Canadian law implications with this investigation as it is a technical investigation done by engineers, not lawyers.