if it is a first, the answer is no. if it is a second or beyond the answer is yes you have been convicted of a crime.
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If it is a first violation, it is considered a traffic violation. If you have more that one, you should definitely disclose any OWI's after your first, as those are not considered traffic violations.
Technically speaking, if you only have 1 OWI, you would not have to disclose it, as the question specifically excludes traffic offenses. However, the presence of the word "minor" is vague enough that I would say the "safe" route would be to disclose it anyway. Many times following this question there's a follow up that states that if you answered "yes," you should list the offenses. Best bet would be to mark "yes" and disclose "noncriminal OWI - 1st, a traffic offense." At that point you're highlighting that it's a noncriminal traffic offense.
The risk you may run by not disclosing it is that the employer views an OWI - 1st as something greater than a "minor traffic violation." If it did that, and you didn't list it and they found out about it, they could technically argue that you falsified your application by not disclosing it. That sounds like a drastic, bleak possibility, but it's a possibility nonetheless.
Hope that helps. If you are denied the job and the employer tells you it was because of your "background" or anything similar, contact an employment law attorney (such as myself) immediately.
James A. Walcheske
Walcheske & Luzi, LLC
This answer was provided for general informational purposes only, and should not be construed or interpreted as providing legal advice or as creating an attorney-client relationship.