I had sole custody and still needed the letter. Canada is weird like that.
I don't remember it word for word anymore but basically you need the letter to say the Child's full name and Father's full name, giving Mother's full name permission to move the child's name permanently to the US.
Now like Boiler mentioned this letter is not full proof. My lawyer did not trust my ex with all his BS so once he signed the letter of consent my lawyer took it to the judge and had him make it a court order.
Check your country's laws with a quick consult with a lawyer.