On Thursday, the judge in the case agreed with a defense motion asking that the arrest video and transcript not be released to the public.
Travis' lawyers have previously said the singer has a great deal of respect for law enforcement and has stopped drinking alcohol.
The August accident was among a string of recent run-ins with the law for Travis.
Police in suburban Dallas cited Travis following an Aug. 23 incident in a church parking lot in which he allegedly intervened in an argument involving a woman he knows and her estranged husband. Nobody was hurt.
Larry Friedman, one of his attorneys, said Travis pleaded no contest in that case in January. In an agreement with prosecutors, he got 90 days' deferred adjudication, meaning it will be removed from his record if he does not get involved in another assault in that time period.
Travis also was arrested last February in Denton County, northwest of Dallas, for public intoxication after police spotted a vehicle parked in front of a church and found an open bottle of wine and Travis smelling of alcohol. That case is no longer on file with the county court and appears to have been dismissed.