What does the law have to say about testing DNA to clear someone of murder after the execution?

I've heard it said that there are no known cases in which DNA evidence cleared someone of murder after the person was executed for the murder. I don't know whether it's true, but if it is, could the reason be that there's some sort of law against it for some reason? Spending money on a posthumous investigation won't bring the wrongly executed person back to life, and the prosecutor would rather not be humiliated.