Mr. Liu, 45, was taken into custody by Minneapolis police on Friday and released the next day. "An investigation by local police did not find any evidence of misconduct, and he will continue his trip as planned".
"During a business trip to the United States, Mr Liu was questioned by police in Minnesota in relation to an unsubstantiated accusation", the company said. The alleged assault would be a felony, authorities said, declining to provide further detail. Liu was never accused of any wrongdoing in that incident.
Minneapolis police said on Sunday that "an active investigation" was underway, although it was possible for the billionaire founder of the firm to leave the United States.
It said Liu had been participating in a business activity at the time when false accusations were made against him, and that a police investigation had not found any inappropriate behavior.
JD.com, the company in which Liu has a large controlling stake, told the Reuters news agency on Monday that he was back in China and back at work. He had to shut it down in 2003 after severe acute respiratory syndrome struck China causing people to stay at home for fear of catching the deadly disease, the Hong Kong based South China Morning Post reported.
Boasting backers that include Google, Walmart, and Tencent, the company claims 300 million active users and a net revenue of 362.3 billion yuan ($53 billion) in 2017.
In June, Google announced it would invest more than half a billion dollars in JD.com as part of a move to expand retail services around the world.
Liu's arrest came shortly after he tried to distance himself from a different sexual-misconduct scandal.
Zhang, described by Chinese media as 24, shot to fame while a student in 2009 when a photo of her holding a cup of milk tea went viral, giving her the nickname "sister milk tea".
Longwei Xu was found guilty in July of sexual assault after a jury found that he pinned the woman down and repeatedly tried to have sex with her during an hour-long ordeal at his hotel room in December 2015, Sydney Morning Herald reports.