The U.S. attorney in Los Angeles has launched a federal grand jury investigation into Cardinal Roger M. Mahony in connection with his response to the alleged molestation of children by priests in the Los Angeles Archdiocese, according to two law enforcement sources familiar with the case.

One federal law enforcement source said such a prosecution could be brought under a federal statute that makes it illegal to “scheme . . . to deprive another of the intangible right of honest services.”