Osborne was investigated at the request of the Matagorda County District Attorney's Office for what it called allegations of misconduct that happened in February.
The investigation was presented to a Matagorda County Grand Jury and Osborne was arrested by the Texas Rangers Tuesday, according to jail records.
"Unfortunately, this case is in the criminal justice system, so I feel I cannot comment except to say that the offense report of the arrest by the officer was not destroyed, concealed, removed, or otherwise impaired and was always available," Osborne said in a statement. "I will say I simply tried to correct a mistake and I look forward to a trial in this matter."
Osborne was booked into jail Tuesday and was released on a $5,000 personal recognizance bond.