The Lawbreaker would go to the one who cast the transformation magic, I'd say. These laws focus on seperating the mortal mind/spirit from the mortal body, and that had already been done by the transformation. If there was no mind left, then presumeably the soul would have departed with it, and no Law was broken.
That said, the Wardens might have a different take on the matter. If, for example, the Dog Formerly Known As Human was someone important, and the mind and soul had been stored in the hopes of reuniting them with the body in some restorative ritual ... well, they might take offense to destroying the chance to repair the damage done, and might have their own interpretation as to whether or not the Law had been broken.
Note, by the way, that if you alter the situation a bit, there *could* be the problem you are talking about. For example, if a Wizard had shapechanged himself into a dog (but was still quite definitely a human underneath the shape of the dog), then someone who killed him would still be breaking the First Law.