I don't think there's a law like this, but I do know that the standards for carseats are independently arrived at in the US and Canada, and thus it's not clear whether a carseat meant for the US would meet the Canadian standards and vice versa.
It's just way easier to buy items that are manufactured for your market than it is to try to figure out whether it's approved. Try arguing with the maternity hospital when they look for the seal of approval sticker or whatever it's called when you are ready to leave with your newborn (yes, my hospital actually inspected my carseat)... "it's new and it cost $200 in the US" just doesn't persuade them.
So you may need to give your SIL a pass on this one...