PORT HURON, Mich.—A lawsuit arguing that the federal bailout of American International Group Inc. is unconstitutional will be allowed to proceed in a federal court in Michigan.

The decision, handed down last week in the U.S. District Court for the Eastern District of Michigan, was made after a judge determined it was unconstitutional for AIG to receive the bailout funds from the U.S. government because AIG has subsidiaries that sell insurance designed to comply with Islamic law.

The suit, filed in December by Kevin J. Murray—a Michigan resident, a former U.S. Marine and a Catholic—alleges the U.S. Treasury Department and the Federal Reserve Board violated the Establishment Clause of the First Amendment. Mr. Murray, who filed the lawsuit “as a taxpayer,” alleged that the “appropriated funds (to AIG) are being used to finance Sharia-based Islamic religious activities” and are therefore “constitutionally impermissible,” according to court documents. ....