Conjoined Twins are identical twins who share some physical connection. In particular, some share the same body, although both possess separate heads. As such, what are the legal ramifications for dicephalic twins, inasmuch as personhood, citizenship, and criminal prosecution are concerned?
Well they are two distinct people, as you reveal by using plural verbs throughout your question. I don't think anyone would endeavour to argue that two conjoined twins, each possessing his own head, mind and personality, are in fact one person (is that your question?).
The difficulty is criminal prosecution. Of course the guilty twin can be proceeded against and tried, but he cannot be incarcerated without unlawfully abridging the freedom of his (innocent) twin. In many jurisdictions this is simply unacceptable.
The only example I was able to track down was this headline:
Judge Releases Siamese Twin To Avoid Jailing His Brother
Unfortunately, it is behind a paywall.
If it is somehow unclear which twin is responsible for a crime committed by one of them, then in any common law jurisdiction—absence proof that they acted together—they must be both be acquitted.