The justices on Monday left in place a federal appeals court ruling that blocked parts of the law. Justice Antonin Scalia voted to hear the state's appeal.
The law's purpose was to reduce the "number of illegal aliens" in Alabama
The Atlanta-based 11th U.S. Circuit Court of Appeals said immigration law primarily is the responsibility of the federal government and that the state lacked the authority to enforce the challenged provisions. The appeals court ruling followed last year's Supreme Court ruling that blocked some parts of Arizona's immigration law.