The suit claims safety failures at a laboratory researching bats in Wuhan led to the release of the virus, and the Chinese government withheld information, and made misleading statements about the disease.
Sheriff Edwards claims the pandemic has reduced the sheriff's office's revenue.
U.S. intelligence officials say there is no indication the virus originated in lab, but believe it jumped from animals to humans at a Chinese "wet market," open-air slaughterhouses where wild animals are sold as meat.
Gov. Edwards says his brother has not discussed the lawsuit with him.