If they commit a crime, a judge and/or jury, informed by the testimony of medical experts, determines whether someone was cognizant of right and wrong. This is not uncommon in the criminal justice system.
Now, responsibility on the larger scale is indeed murky. We societally at once say addicts are and aren't responsible for their behavior (depending upon one's point of view and what acts took place): a drunk driver is treated differently than a homeless addict living under a bridge. Is Kanye 'addicted' to manic states? Should we look down upon him because he won't take his meds? I'm not sure.