The debate over how to sift out illegal voters from legal ones has reached the federal appeals court level, making it possible the Supreme Court eventually will rule whether a state can demand a birth certificate to register to vote. The case before the 10th Circuit Court of Appeals in Denver centers on a 2011 Kansas law, the Documentary Proof of Citizenship (DPOC). In June, a district court judge struck down the law, with biting criticism of analysts who contend a large number of noncitizens nationwide vote illegally, tilting close elections to Democrats. Judge Julia A. Robinson said the Kansas...