Excellent answer, Northern Piper, but I’ll put a finer point on it, if I may.
Rbroome, Ontario cannot pass a criminal law. That privilege is reserved to the federal Parliament (Constitution s. 91(27)). Criminal law is federal, which means that it is uniform across Canada. If convicted of a criminal offense, a person has a criminal record in all of Canada, not just in Ontario or Alberta, or wherever.
Provinces can enact laws that result in provincial offenses (which do not result in criminal records), and Northern Piper has addressed this. But they cannot pass criminal laws. There’s really no need to, as the Criminal Code of Canada is quite large, and encompasses pretty much every crime possible.