There are laws that require children to wear bike helmets, but there aren't laws that require parents to make sure helmets fit properly. And a proper fit is as important as a proper helmet.
Make sure that your child's helmet fits snugly, but is not too tight. The straps should go over the ears, not on top of them. And your child needs to understand that the helmet must remain parallel to the ground, not pushed backwards on the head. The helmet should cover the forehead and be strapped so it stays that way. Make sure your child has a say in picking a helmet, so he or she likes it enough to wear it.
Click here for more info on child safety.