Say my conjoined twin commits a crime-not a murder or anything I witnessed or participated in, but something like embezzling money via the internet that merits a jail sentence. If convicted, how would the justice system handle this?
As you might expect, nobody really knows. We have no precedent for this, at least in the Anglo-American body of law.
I think for most crimes, perhaps all crimes, the non-guilty twin would have a good argument that any punishment, especially imprisonment, would be unlawful. If the State has to choose between letting a guilty person free or imprisoning an obviously innocent person, the choice is easy.
It’s not so easy if the evil twin is a real danger (murderer, child molester, etc). Perhaps it would depend on whether the good twin had the ability to stop the bad twin from committing crimes, although normally, we have no duty to stop another from criminal conduct. (absent special circumstances)
This scenario was once presented to me as “lateral thinking question”. A judge finds a man completely guilty and deserving of jail time, but lets him go because jailing him would be an injustice. The answer was because he was a conjoined twin and his sibling was completely innocent.
I have yet to see a more authoritative legal opinion on the matter. 
A complication would be if the “good” twin had been the victim of the crime.
If the question was worded exactly like that - “jailing him would be an injustice” - then it was misleading, perhaps deliberately so. Jailing the guilty twin would be justice, but it would cause an injustice by simultaneously incarcerating his innocent twin.
Since the two had already been condemned by a higher court to be the prisoners of each other, they are together destined to such fates as may befall either of them.
The conjoined twin committed conspiracy to commit (whatever). What a coincidence that the judges’ sentences in both cases is the same punishment!
Not necessarilyy. Twin #1 could commit the crime while twin #2 takes a nap, or plays a video game, or otherwise completely avoids participating in the crime.
The OP explicitly sets up the scenario as one in which twin #2 is an innocent bystander (albeit at very close proximity).
its the basis for one of the plotlines in the movie chained for life starring real conjoined sisters daisy and violet hilton.
mc
That’s not an answer to the question-that’s just a rehash of the dilemma. The question is what should happen if one is guilty and the other is not?
Since you can’t lock up the bad twin without locking up the good twin I’d say use the iron mask with just a breathing hole on the bad one.
Punitive lobotomy. (Make sure you don’t get the heads mixed up)
Realize that if you mentally impair one that will likely have a large impact on the life of the other.
Locking up the good twin would be a pretty clear constitutional violation. Generally, we do not permit constitutional violations unless there is a really good reason, and locking up someone convicted of a crime often isn’t enough.
So while it’s true that there’s no definitive answer, I’d say the good twin has a very strong legal argument and is likely to prevail.
Are conjoined twins considered 2 legal persons? Do they need 2 passports, can they both vote?
Yes. Two driver’s licenses too, which might make it difficult for a cop to decide who to give a speeding ticket to.
I am imagining they might send the conjoined twins to jail, but the one who does not deserve to be there might get special privileges while someone supervises to make sure the bad twin doesn’t get to enjoy it.
It would be interesting in the case of the death penalty, if there might be some way of cutting off the other twin so the remaining twin can still be alive.
You give it to the one on the left, at least in this country.
Now you’ve got me thinking. What if one conjoined twin sexually assaults the other? I suppose that would be considered incest, but how do you punish the bad twin and how do you protect the good twin from the bad one going forward?