U.S. Courts do not apply Islamic Shari'a law because it violates the Establishment Clause set in the United States Constitution; they apply foreign law when necessary. American Courts do apply foreign law in certain cases involving international principle known as "conflict of Laws," or "Private International Law." This is referred to in U.S. courts as "the doctrine of comity".
In the area of Private International Law, Comity is a courtesy, amity, and reciprocity by U.S. courts towards court decision issued in other nations. Such a consideration by U.S. courts does not entail an obligation to agree with the rulings of foreign judgments. There is therefore a distinction between the doctrine of comity and law.
Public International Law can become part of the national law when the country has its signature on that law, Private international Law however, does not have the same level of recognition by U.S. Courts. The issue of comity is raised in Islamic divorce cases when a person who resides legally in the United States travels to a foreign country and obtain a certificate of divorce from a religious court.
The intent is to obtain an instant divorce by pronouncing triple talaq (divorcing his wife three times in a few minutes.) Such an action leaves the wife with nothing more than a nominal deferred mahr, and takes advantage of the child custody, which discriminates against the women and to label the wife as bad Muslim.
The man then returns to the United States and serves his wife with divorce papers demanding the implementation of the divorce according to the Islamic Shari'a, claiming that the "doctrine of comity" applies to his case.
Generally, a judgment of divorce for example issued in a foreign country is recognized in the U.S. on the basis of comity, provided both parties to the divorce received adequate notice, i.e. service of process and, generally, provided one of the parties has a domicile in the foreign nation at the time of divorce, and the foreign court has given opportunity to both parties to present their case, and the trial was conducted upon regular proceedings after due citation or voluntary appearance of the litigants, and under a system of jurisprudence likely to secure an impartial administration of justice between the citizens of its own country, and those of other countries, an no prejudice towards either party and should not violate a strong U.S. principle of law, and the parties were present in court. The court may deny the application of comity if the judges deem the foreign laws is "repugnant" to U.S. principle of law.
An Islamic triple talaq differs substantially with respect to property division. Under Islamic Shari’a, wives may be entitled to a deferred mahr, which is, in most cases, much less than what U.S. courts order; above all, U.S. courts will not accept an Islamic divorce certificate obtained in a foreign country if the cause of action on which the divorce is based is "repugnant" to the public policy of the State in which the case is litigated.