But first you will have to prove that the other is 100% inocent. After all a act of crime must be punished. It might be argue depending on the crime, which part of the body was used to comit that crime. This comment has lots of credit
For the one twin to be innocent, the other twin who committed a crime could have knocked the other one out or physically incapacitated the innocent party.)
because if both are awared of the action, then one cannot be inocent. If one is indeed innocent then it must be that at one point the inocent one must have been unconsiouse of the event.
Makeing the guilty one the only conscious mind at the crime.
A suitable punishment will be, to drug the guilty one. Becasue you cant jailed them, for the inocent will also be punished. You cant only mentally punished them.
The question of whether or not one can do something is not a moral argument, rather an argument of capability. The justice system is surely capable of charging the innocent twin with being an accomplice or accessory. I imagine the innocent twin would be charged with the thought of mens rea in mind, regardless of the actus rea. If he is judged to contain the mens rea, meaning that the didn't stop their twin, and they committed the crime by proxy and therefore were mentally capable and willing of the crime.
This may not be ethically right, but the question was worded in a manner that suggests the capability of the system to pin a crime on an innocent. It's definitely possible. Let's use Cameron Todd Willingham as an example. He was wrongfully charged and executed. He didn't set that fire and he was not ultimately responsible for the deaths of his children. He was still convicted and executed.
Substituting "is it permissible" for "can," I still agree that you can punish the guilty twin at the expense of the innocent twin. The crux here is that any kind of punishment of the guilty party will negatively affect his conjoined twin--this is unavoidable. But all punishment is similar. There are always (or very often) innocents who are damaged by the punishment of the guilty. Even in a moral system that moved beyond "punishment," the rehabilitation of the guilty twin could have immediate negative effects on the innocent twin, just as the time spent recovering from an illness affects not only the diseased but also his friends, family, co-workers, customers, and so forth. Your question brings home the fact that no man is an island, but the analysis cannot change simply because of a physical connection. There would be some limitations as to the taking of life or liberty, but the idea that punishment (or in a better world, rehabilitation) would be prohibited is incompatible with how we treat the question in general.
One has to devise a scenario where this is even possible. Let's say the one twin stabbed his wife while the other twin slept comfortably next to his until morning when he found out. But how can we say the sleeping twin was innocent? Did he not notice his twin pick up the knife, or the problems leading up to the incident, or the homicidal nature of his twin? In the end one might have to look at how innocent the other twin really is. Still if no determination is possible a mental facility might be in order. There are other scenarios, such as a bar fight or a dui that also bear this pattern in my mind. A twin should not be incarcerated for the other's crime--but he is in some sense responsible and should be considered alongside any ruling.
If one twin is imprisoned, the other must be too, regardless of the innocent status,and our justice system is dedicated to protecting innocent, punishing the guilty, not punishing the innocent and guilty. As such, it would be immoral to punish the innocent for a crime they are innocent of, but they could be an accessory.