Referring the question to Dr. `Abdul-Fattah Idrees is a professor of comparative jurisprudence at Al-Azhar University,

In a Muslim country that practices Islam, observes its rulings and safeguards the application of shari`ah, both Muslims and non-Muslims are subject to the Islamic law. Killing, stealing, rape and the like crimes will punishable according to the Islamic Shari`ah.

As for the things that are haram and punishable for Muslims but the non-Muslims believe in their permissibility such as drinking alcohol or eating pork, the Islamic legal penalties are not applied to the non-Muslims in this regard unless they publicize such practices violating the general feeling of the Muslim community, in which case the Muslim ruler may punish them to deter them from causing harm in the society.