(CNN) Relatives of notorious Depression-era American gangster John Dillinger plan to exhume his body because they want to confirm whether it's him buried in an Indiana cemetery, according to affidavits filed with the Indiana State Department of Health.

The department approved an application submitted by Dillinger's nephew on July 3. His body is buried at Crown Hill Cemetery in Indianapolis, according to the permit.

Mike and Carol Thompson say in the affidavits that they are Dillinger's nephew and niece, respectively. They claim to have evidence that the person shot at the Biograph Theater in Chicago on July 22, 1934, "may not in fact have been" Dillinger. The affidavits say that several of the man's physical attributes, including eye color, fingerprints, anterior teeth, ears and head shape, did not match Dillinger's.

The FBI's Chicago office disputed the theory that agents got the wrong guy.

"A wealth of information supports Dillinger's demise including 3 sets of fingerprints, all positively matched," the FBI tweeted Thursday.

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