Depends on the maturity level. I know that they really aren't supposed to babysit until around 14-ish.
Call your local police department or sheriff's office for the laws in your area.
There are also babysitter prep courses given through hospitals sometimes that might be familiar with this type of thing. Those courses offer CPR and first aid for kids that would be babysat so you would end up with a better babysitter.
I thought my 11 1/2 year old was pretty mature, until he and his friend were caught in the front yard with a lighter and a spraycan of deoderant. He will be 12 this summer. Now I wouldn't let him babysit, but thought that he was a bit more responsible than that. So you can really never tell. And I was home in the house BTW. You would think that he would even be smart enough to wait until I wasn't so close by. So I really had to re-think his maturity level and responsabilities, privledges, peer pressure, etc. Girls can be a bit more mature. I was babysitting at 12 and 13, with no problems. But again, I would check with the police stations and go from there.
Good luck,
L.