Sheikh `Abd al-`Azîz al-Fawzân, professor at al-Imâm University
If a Muslim judge is appointed by a non-Muslim country to issue judgments among Muslims in accordance with Islamic Law, then it is obligatory for the Muslims under his jurisdiction to abide by his rulings. Arbitration among people is something essential in order to protect and safeguard people’s interests.
This is something quite valuable for the Muslims who live in that country. They have to arbitrate to him and abide by his rulings as long as his rulings are in compliance with Islamic Law. However, in case this judge is forced to rule by the laws of that non-Muslim country, then it is not legal for him to do so and the Muslims will not be obligated to abide by his rulings. In fact, in this case Muslims will be not allowed to appeal to him.
As long as he passes judgment according to Islamic Law, we may not argue that because this judge was appointed by a non-Muslim country, Muslims may not resort to him. In this way, the muslims would remain without a judge to solves their problems and determine their rights.
Scholars have decided that if Muslims live in a non-Muslim country where there is no Islamic court available, and they come in need of arbitration for their rights then they may arbitrate to the non-Muslim court in order to attain the rights that are rightfully theirs according to the Islamic Law. Since it is permissible to arbitrate to a non-Muslim court as long as it rules by justice and gives everyone his right, it follows logically that arbitration to the Islamic judge who is appointed by the non-Muslim government will be permissible to a far greater extent.
And Allah knows best.
Source: Islam Today