Interesting question: "Who is responsible for the murder of King Duncan?" Of course Macbeth wields the murder weapon and does the deed, so he is ultimately responsible for the crime. There is no question, however, that Lady Macbeth, in at least a legal sense, is also responsible. This may be of interest to you:
At law, an accomplice is a person who actively participates in the commission of a crime, even though they take no part in the actual criminal offense. For example, in a bank robbery, the person who points the gun at the teller and asks for the money is guilty of armed robbery. However, anyone else directly involved in the commission of the crime, such as the lookout or the getaway car driver, is an accomplice, even though in the absence of an underlying offense keeping a lookout or driving a car would not be an offense.
An accomplice differs from an accessory in that an accomplice is present at the actual crime, and could be prosecuted even if the main criminal (the principal) is not charged or convicted. An accessory is generally not present at the actual crime, and may be subject to lesser penalties than an accomplice or principal.
If a court of law were involved in the case of the murder of King Duncan, Macbeth would be found guilty of murder. Whether Lady Macbeth is found to be an accomplish or an accessory depends on how good her lawyer is :-)