Two years later, Jones, an attorney and former executive for the internet hosting company GoDaddy, was convicted on a pair of misdemeanors, according to the newspapers.
"There was no one in the car with me at the time, there was no accident and fortunately no one was hurt," Jones said in the statement to the publications on Tuesday. "I went to court and paid my dues like everyone else. It is a mistake that I very much regret and I am not proud of that night."
The Capitol Times also noted that Jones had the middle name of Elizabeth at the time of her arrest, but that court records show she legally changed it to Newman in 2009.
Last week, Jones made headlines when she serenaded Maricopa County Sheriff Joe Arpaio (R) at a charity event and botched some facts about Arizona.
Jones is running in the 2014 race to replace Gov. Jan Brewer (R), who will be leaving office due to term limits.
This post has been updated.