SAN FRANCISCO (Reuters) - A former chief executive of Calpers, the largest U.S. public pension fund, was indicted on federal conspiracy charges in connection with a scheme to commit fraud, the U.S. Department of Justice said on Monday.

Former Calpers CEO Federico Buenrostro was indicted by a San Francisco grand jury, as was Alfred Villalobos, a former member of the pension fund's board. They were charged in connection with the scheme involving fraudulent documents related to a $3 billion investment by the retirement system in funds managed by Apollo Global Management.

The private equity company had hired Villalobos' firm, ARVCO Capital Research LLC, to provide placement agent services to secure investment business at the pension fund, formally the California Public Employee Retirement System. He and Buenrostro conspired to create fraudulent investor disclosure letters sent to Apollo, according to a statement released by the U.S. Attorney for the Northern District of California.

Apollo paid ARVCO about $14 million in fees after receiving the fraudulent letters, the statement said, adding that ARVCO transmitted the last of the letters in June 2008, a few weeks before Buenrostro retired from Calpers and was hired by Villalobos to work for ARVCO.

The statement also said the two men made false statements to authorities investigating the disclosure letters, adding that the grand jury charged Buenrostro with making a false statement and obstruction of justice.

The U.S. Securities and Exchange Commission last year charged the two men with scheming to defraud Apollo.

Buenrostro's lawyer and representatives for Villalobos could not be reach for comment.

Apollo and Calpers have cooperated with long-running federal and state probes of placement agent activity at the pension fund, and the investigations spurred it to increase its oversight of placement agents.

"We are extremely pleased that law enforcement authorities are moving to hold individuals accountable for activities which violate the public trust," Rob Feckner, president of the Calpers board, said in a statement.

Apollo said the allegations in the indictment are "troubling" if true.

"Apollo has always followed best practices in handling its placement agent relationships, and was not aware of any misconduct engaged in by Mr. Villalobos during the time that he worked with Apollo," the company said in a statement.

(Reporting by Jim Christie; Editing by Gary Crosse, Steve Orlofsky and Tim Dobbyn)