The lawsuit contends that Badal had command and control of law enforcement officials, who "inflicted cruel and inhumane treatment and extrajudicial death" on three named plaintiffs and thousands of other unnamed members of a requested class of plaintiffs, the Journal Sentinel newspaper here said.
Badal is visiting Milwaukee for a wedding and to attend the funerals of victims in Sunday's Gurdwara shooting in which six Sikhs were killed.
The 30-page complaint was filed in US District Court in Milwaukee by Avtar Singh of New York, who lists himself as coordinator of "Sikhs for Justice."
The daily said Badal declined to comment about the suit, saying he hadn't seen it.