If my sister died with no will, and my name is on her checking account, she is not married and has no child, who does the money belong to?

Well, that depends. If she had a will when she died that listed her bank account as an asset, the terms of the Will would govern who gets the funds in the account. On the other hand, if she died intestate (no written will), you would have a claim to the funds as a joint account holder. You should consult with a lawyer who does probate cases to figure this out.

It sounds like, either way, the money is yours. There is a presumption that the surviving owner of a joint bank account owns the account on the death of the other owner. If that wasn't actually what she intended, then you still probably inherit, unless your parents are alive. Parents would inherit first, but if they have already passed away, then brothers and sisters. If you don't believe she intended for you to have the money when she passed away, you should share it equally with any brothers and sisters.