Siamese Murder

Senario: One half of a Siamese twin murders someone.

So what do you do?
If one half didn't try to stop the other then they are both guilty. One half would be called an accessory to murder and hence punished less than the actual murderer. So if one gets 10 years in jail and the other gets 40 what do you do?

On the other hand, in some countries there is the death penalty for murder but not for being an accessory. So you kill one half and the other will probably die too which then makes the state government guilty of murdering someone unworthy of such punishment!

But what if one half was asleep or tried to prevent the other from murdering? Is that provable? Wouldn't the aliby be the murderer. What if he confesses and says the other didn't do it - does that mean he gets off too? Surely you can't punish an innocent person. But surely a guilty person must not go unpunished.

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Answers as comments please!