According to online records, Crawford was charged via summons on March 27 and pleaded not guilty on April 12.
The incident took place on March 15, according to a complaint affidavit. TMZ published video that shows Crawford fighting with members of the security staff at Coyote Ugly Saloon.
According to the affidavit, there was a fight between patrons and bar security that spilled out on to the street. The affidavit alleges that Crawford "charged toward" an officer who was attempting to restrain a member of his party "and pushes in between the officer and the defendant's party," hindering the officer "from detaining this individual."
A pretrial conference is scheduled for June 13 in the case.
The Cowboys had no comment when contacted by ESPN.
According to the NFL's personal conduct policy, a player can be subject to a fine or suspension whether convicted or not, if credible evidence establishes a player engaged in prohibited conduct.
Crawford, 29, started 15 games last season and finished with a career-best 5.5 sacks.
ESPN's Dan Graziano and Todd Archer contributed to this report.