Dallas police said Tuesday the reporting party had signed an affidavit of non-prosecution over the incident at a downtown nightclub, but that the investigation is continuing.
Law enforcement officials have told The Dallas Morning News that Rice was suspected of assaulting a person early May 6, and that the person went to a hospital after the encounter.
Dallas police did not name Rice as the suspect in detailing a report of the incident to The Associated Press.
Rice's attorney, Texas state Sen. Royce West, didn't respond to a message from the AP seeking comment. The NFL declined to comment.
Rice reported to the Chiefs for voluntary workouts last month, not long after turning himself in to Dallas police over multiple charges, including aggravated assault, involving the high-speed crash.
West has previously acknowledged Rice was speeding in a Lamborghini SUV when the crash involving six vehicles happened March 30. Police said Theodore Knox was driving a Corvette.
According to a Texas Department of Transportation report, Rice was driving the Lamborghini at a top speed of 119 mph before impact, while the Corvette that Knox was driving had a top speed of 116 mph.
Rice, a former SMU and Dallas-area high school player who turned 24 last month, and Knox have been charged with one count of aggravated assault, one count of collision involving serious bodily injury and six counts of collision involving injury. Knox also played for SMU.
Four people were injured in the crash, and police said the occupants of the Lamborghini and Corvette left the scene without providing information or determining whether anyone needed medical attention.
Rice was drafted in the second round by Kansas City last year and played in 20 games, including the Chiefs' 25-22 overtime victory over San Francisco in the Super Bowl. He led the team with seven touchdowns receiving in the regular season.