Is it permissible for non-Muslims residing in Islamic countries to seek judgment according to their own law, or must they be compelled to seek judgment according to Islamic Sharia?

Disbelievers residing in Muslim lands are not compelled to abide by the rulings of the Muslims; rather, they are judged among themselves according to their own law. If a dispute arises between a Dhimmi and a Muslim, it is obligatory by consensus to judge between them according to Islamic law. Scholars differed on whether it is obligatory to judge between them according to our law if they refer their case to us. Some said it is not obligatory, based on the Almighty's saying: "If they come to you, you may judge between them or turn away from them. And if you turn away from them, they will not harm you at all. But if you judge, judge between them with justice." This is the view of the majority. Others said it is obligatory, based on the Almighty's saying: "And judge between them by what Allah has revealed," claiming that this verse abrogates the first. If disbelievers refer their case to us along with a Muslim, it is necessary to judge between them to ensure justice for the Muslim. However, if they engage in invalid sales and have already taken possession, their action is not nullified. If they have not taken possession, the ruler annuls the contract. If they engage in usurious transactions in the Muslim market, they are prevented from doing so.