Glushchenko, who belonged to the Liberal Democratic Party, is suspected of organizing the murder of businessman Yury Zorin, translator Viktoria Tretyakova and fellow former LDPR Deputy Vyacheslav Shevchenko in March 2004, the Investigative Committee said in a statement.
The victims' bodies were found wrapped up in plastic bags in a bathroom at a private villa near the town of Davos.
Glushchenko was detained in St. Petersburg on Tuesday when he went to a police station to get a new passport.
Glushchenko's name previously surfaced in an investigation into the 1998 murder of liberal Duma Deputy Galina Starovoitova. In 2004, a witness in the Starovoitova case accused Glushchenko of helping order her killing.
Glushchenko served in the Duma from 1995 to 1999, and LDPR leader Vladimir Zhirinovsky said Wednesdday that he had had no dealings with him since that time.
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