Lawsuit says buyout firms colluded on deals

But after KKR showed interest in Freescale, Blackstone readied a bid for HCA, an apparent attempt to retaliate. The complaint alleges that executives at Blackstone and KKR then talked and decided not to compete against each other.

Once Freescale accepted Blackstone's bid of $40 a share, Hamilton James, Blackstone's president, sent an email to George Roberts, one of KKR's founders. "We would much rather work with you guys than against you," James wrote. "Together we can be unstoppable but in opposition we can cost each other a lot of money."

"Agreed," Roberts replied.

Although the complaint names a number of executives at Bain, it makes no mention of Mitt Romney, the Republican candidate for president and one of Bain's founders.

The court papers were released following a request from the New York Times.