Mills, 44, died Saturday after he was shot by Pit and Barrel bar owner Chris Ferrell, 44, police said.
Ferrell told police he and Mills had argued about smoking inside the bar.
"We're investigating Chris Ferrell's claims of self-defense," said Kris Mumford, a police spokeswoman.
Ferrell was previously arrested twice for driving on a suspended license and Mills had prior convictions for driving under the influence and reckless endangerment, The (Nashville) Tennessean reported Monday.
Mills was the singer for the Wayne Mills Band, which often played the college circuit in the area. Country music stars Jamey Johnson, Blake Shelton and Taylor Hicks were the opening acts for the Wayne Mills Band early in their careers, the newspaper said.
"Extremely sad to hear about the death of my old friend Wayne Mills," Shelton said in a message on Twitter Sunday.