e-commerce company JD.com, attends a France-Chinese forum on the applications of artificial intelligence at SOHO 3Q in Beijing, China January 9, 2018.
Elder declined to provide details about the allegations but said authorities are not overly concerned about Liu leaving the country.
A Minneapolis police department spokesperson said over the weekend the investigation was "active" but Liu hadn't been charged.
JD.com said in a statement on Sunday on social media that Liu was falsely accused while in the USA on a business trip, but police investigators found no misconduct and that he would continue his journey as planned.
JD.com is China's second-largest e-commerce company after Alibaba.
Liu built JD.com from scratch.
JD.com, backed by Walmart, Alphabet's Google and China's Tencent Holdings, said in a statement on Sunday that Liu was falsely accused.
The arrest comes shortly after Liu was in the spotlight for another incident involving sexual misconduct. Liu was detained on Friday and released on Saturday. The two tech firms plan to join forces to sell goods online across Southeast Asia, the United States and Europe in order to better compete with rivals like Amazon and Alibaba.
The University of Minnesota said Liu was a student in its doctor of business administration program, which primarily takes place in Beijing in partnership with Tsinghua University and is aimed at full-time executives. "Milk Tea Sister" and Liu met while they were studying in New York City and later married in Australia. He is also known for his marriage to Chinese internet celebrity Zhang Zetian.
Earlier this year, Liu attempted to suppress information about a sexual assault that occurred after a 2015 party at his Australian home.
Longwei Xu, a property developer, was later convicted of the crime.
The firms will marry JD's supply chain and logistics experience with Google technology to create "next generation" personalised retail service in regions including Southeast Asia, the U.S. and Europe, both companies said in a statement.