According to court documents, Leary was arrested in Irving, Texas, on Sept. 7, 2012, two days after the Cowboys' season opener at the New York Giants.
There has been numerous court dates postponed since the original arrest. Leary, who was a rookie practice squad player at the time of the arrest, didn't get promoted to the active roster until that December.
When an NFL player is charged with a DWI offense, he's placed into the league's substance abuse program. Once that player completes the program, the league considers the legal matter over based on the facts of any particular case.
Adisa Bakari, Leary's agent, and Cowboys' officials declined comment.
The Cowboys had three players arrested for DWI charges within a five-month period two years ago.
On Jan. 22, 2013, defensive lineman Jeremiah Ratliff was charged with DWI in Grapevine, Texas, after hitting a tractor trailer.