According to the teachings of Islam, Muslims and non-Muslims – who live in the Islamic state – are treated equally. Religion doesn’t make difference in applying the hudud or penalties and punishment in the Islamic state. If a Muslim, for example, kills a non-Muslim with no right, he has to be killed in retaliation, and vice versa.
Sheikh `Abdul-Majeed Subh, a prominent Azharite scholar, states the following: All people, Muslims and non-Muslims, are equal before the Shari`ah with regard to penalties and punishments.

Scholars of Islam say that if a Muslim kills a non-Muslim unjustifiably, he has to be killed by the Islamic authority in charge of applying the penalties. The same is true also regarding killing a non-Muslim in retaliation if he kills a Muslim unjustifiably. This is according to the general instruction of the Qur’anic verse: (And We prescribed for them therein: The life for the life, and the eye for the eye, and the nose for the nose, and the ear for the ear, and the tooth for the tooth, and for wounds retaliation. But whoso forgoeth it (in the way of charity) it shall be expiation for him. Whoso judgeth not by that which Allah hath revealed: such are wrong doers.) (Al-Ma’idah 5: 45)
It goes without saying that the above ruling applies to all other crimes and penalties.

For more information, the eminent Sheikh goes further on this issue in his “Good Argumentation with the Doubters of Islam”, published by Dar Al-Manarah, Egypt:

Since the 2nd century of Hijrah, or even before that time, some eminent Muslim jurists as Imam Abu Hanifah have held the view that any Muslim who kills a non-Muslim (a citizen of the Islamic State, under the category of Ahl Adh-Dimmah or non-Muslims having covenant with Muslims) should be killed in retaliation for his crime.
Since the age of Haroun Ar-Rashid, the judge of Baghdad, Abu Yusuf, has proclaimed the opinion that the Muslim who kills a non-Muslim should be killed.
the above legal verdict depends on the general nature in the following Qur’anic verses:
(O ye who believe! The law of equality is prescribed to you in cases of murder: the free for the free, the slave for the slave, the woman for the woman. But if any remission is made by the brother of the slain, then grant any reasonable demand, and compensate him with handsome gratitude. This is a concession and a mercy from your Lord. After this whoever exceeds the limits shall be in grave penalty.) (Al-Baqarah 2: 187)
(And We prescribed for them therein: The life for the life, and the eye for the eye, and the nose for the nose, and the ear for the ear, and the tooth for the tooth, and for wounds retaliation. But whoso forgoeth it (in the way of charity) it shall be expiation for him. Whoso judgeth not by that which Allah hath revealed: such are wrong doers.) (Al-Ma’idah 5: 45)
In the Sunnah, we read also the Hadith narrated by Al-Bayhaqi indicating that Prophet Muhammad (peace and blessings be upon him), killed a Muslim in retaliation for his killing a non-Muslim who had concluded a peace-treaty with Muslims, saying, “I am (the Prophet of Allah) the most honored one who should keep his covenants.”
Likewise, according to the Islamic jurisprudence, the Muslim’s hand should be cut off if he steals a non-Muslim’s property as long as the latter is not at war with Muslims. The prohibition of blood-shedding, of course, is greater than stealing others’ properties.
accordingly, a man should be killed if he kills a woman or a child and a free man should be killed if he kills a slave one.

In the light of the above Fatwa, it becomes crystal clear that the Shari`ah knows no discrimination. All people living in the Islamic state are equal before the Law.