When a person renounces United States citizenship a Certificate of Loss of Nationality is issued.
http://www.state.gov/documents/organization/81609.pdf
That is a public record and anyone can gain access to that record via a Freedom of Information Act request.
Updates:
New Jersey Lieutenant Governor Kim Guadagno has accepted and approved Administrative Law Judge Jeff Masin’s opinion that Ted Cruz is a natural born citizen and thus eligible for the New Jersey primary ballot. The plaintiff has the option of appealing the Lieutenant Governor’s decision to the New Jersey Superior Court.
U.S. District Court Judge for the Southern District of Texas Gray Hampton Miller, a George W. Bush appointee, has dismissed with prejudice (can’t be refiled) the lawsuit of Houston attorney Boris Schwartz. Judge Miller ruled that Mr. Schwartz did not have standing to bring suit against Senator Cruz.
Cruz’s lawyer, Layne Kruse, argued Wednesday that Schwartz had no legal standing to raise the legal question. He told the judge that questions about a candidate’s eligibility for office are the purview of the electoral college and the legislative wing of government, not the judiciary. And he said that Schwartz did not have a cause of action because there was no evidence of direct harm to him from Cruz being on the ballot.