SAN FRANCISCO — When news broke this week that Liu Qiangdong, the billionaire founder of the online retailer, had been arrested in a criminal sexual misconduct case while on a business trip in Minnesota, the local police were vague about the details.

On Tuesday, the Minneapolis Police Department released its report on the case and said Mr. Liu was arrested Friday on a rape allegation.

Mr. Liu, who goes by Richard Liu in the English-speaking world, was freed on Saturday without bail and has returned to China. At the time, the police did not offer specifics beyond using the term “criminal sexual conduct,” which covers a range of nonconsensual sexual contact.

The police report was written the night of Mr. Liu’s arrest, said John Elder, a spokesman for the Police Department, and was released because it is a public record.

“We’re progressing nicely,” Mr. Elder said of the investigation. “There’s a lot that’s been done, and there’s a lot to go.”

The accusation has put under pressure. Its shares fell 6 percent on Tuesday, their first day of trading since news of Mr. Liu’s arrest first surfaced. The company’s stock price was already at its lowest levels since early last year on rising concerns on other fronts, such as increased competition in the Chinese e-commerce business and weakening consumer sentiment.

The case has prompted intense interest among Chinese internet users, who have circulated Mr. Liu’s police photo online and speculated about the details of his case. is one of China’s largest e-commerce sites, and it competes fiercely with the Chinese online giant Alibaba. Mr. Liu’s rivalry with Jack Ma, Alibaba’s co-founder, is a fixture on online forums and in social media. has said Mr. Liu was falsely accused. “During a business trip to the United States, Mr. Liu was questioned by police in Minnesota in relation to an unsubstantiated accusation,” the company wrote in a weekend post on Weibo, a popular social media platform in China.

The Minneapolis Police Department said Mr. Liu had been released pending a formal complaint, noting that the investigation was “really in its infancy.”

A spokeswoman referred on Tuesday to a statement, published before the release of the police report, that noted Mr. Liu had been released without charges and without a bail requirement.

In July, an Australian court rejected Mr. Liu’s request not to have his name released in connection with a sexual assault that occurred after a party at his home in Sydney in 2015. Mr. Liu argued that releasing his name would harm his marriage and business. Longwei Xu, a guest at the party, was convicted of sexual assault this year.