Liu was released without being charged after his arrest on Friday and has returned to China.
JD.com, the company which Liu founded in 1998, is an e-commerce juggernaut in China and the main competitor to industry leader Alibaba.
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The Journal said authorities in Minnesota are investigating a complaint against Liu by a female student from China.
Liu, 45, was in that Midwestern state as part of a residency for a PhD program in business administration offered by the University of Minnesota.
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The Hennepin County Attorney's Office said prosecutors were waiting for the case file from police investigators before deciding on whether to charge Liu, the Journal said.
Minneapolis police could not be reached for comment.
The Minneapolis Police Department over the weekend said the investigation remained active but would not confirm details of the arrest or the allegations against Liu.
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