Smith, 46, has the backing of Sonic’s board of directors, led by his father, company co-founder Bruton Smith, who is executive chairman. In a statement, the board said it “remains steadfast in its support” of the CEO.

“We believe in David’s leadership, honesty and transparency, which he has demonstrated throughout his tenure as chief executive officer and over 20 years of service to the company,” the statement said. “David has informed the board that he is innocent of these charges and expects to be fully exonerated.”

Smith, who leads the nation’s sixth-largest new-vehicle retailer, was arrested about 9:45 a.m. Oct. 5 and taken to jail, according to police and the jail’s website. He posted a $30,000 bond and was released around 4:45 p.m. Oct. 6, according to the website.

The unidentified woman told police she was assaulted and unlawfully restrained without her consent at a home in Charlotte, N.C. The woman, who is not related to Smith, had minor injuries of bruises and scratches and was treated at the scene, according to the report.

David Smith didn’t respond to requests for comment. Sonic’s stock fell 6.8 percent as more than double the usual number of shares changed hands Thursday, Oct. 8, the day following news of his arrest.

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