Police spokespeople said they are continuing to investigate, but Liu is not being held in custody and does not face travel restrictions.
The founder and CEO of the popular Chinese retailer was arrested last week while on a business trip in Minnesota. The jail records do not provide details of the alleged incident. He was released Saturday. He has been released without any charges, and without requirement for bail.
Originally, police had said that Liu was arrested on suspicion of "criminal sexual conduct", a broad term which could include a number of different forms of unwanted contact. He has returned to China, appearing at an event on Tuesday to sign an agreement with Shandong Ruyi, the owner of Swiss luxury shoe firm Bally. JD has not commented on the ongoing investigation but said in previous statements that the police had not found any misconduct in their probe into Liu.
Chuck Laszewski, a spokesman for the Hennepin County Attorney's Office, said prosecutors are awaiting the case file before making any decision about potential charges.
They said they will invite shareholders who suffered losses to participate in the investigation and a possible class action lawsuit.
Liu faces a first-degree felony if he is charged with the crime, according to the Associated Press and the South China Morning Post, citing police records that are not public at the moment.
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Minneapolis police told the BBC on Monday his release was "not indicative of the strength of the evidence". China does not have an extradition treaty with the United States.
"Negative publicity could also compromise JD.com's ability to attract global brands to its marketplace, which has been a top focus of the CEO over the past two years or so", Sanderson said.
The exercise price is US$33.40 per ADR - about US$7 above the current market price - subject to a 10-year vesting schedule with 10 per cent of the award vested on each anniversary of the grant date, according to information in the company's latest annual report which was confirmed by JD.
In an earlier statement posted to Chinese social media network Weibo, JD.com described the allegations as false.
JD.com's shares, now valued at some US$42 billion, have lost around 30% since the start of the year on weaker sales amid stiff competition from much bigger rival Alibaba Group Holding Ltd.
The case involved a person who had been a guest at a party hosted by Liu at his home in Sydney in 2015 who accused another guest of sexually assaulting her at a hotel.