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The DUI may be relevant to your company if this employee will ever have occasion to drive---either with their own vehicle or with a company vehicle----as part of their job duties. Consequently, it might be a good idea to bring up the fact that you are aware of the conviction and inquire whether they have a valid driver's license and car insurance on any cay they might possibly use for business.
Be careful though not to inquire as to whether the employee has an alcohol problem now, or in the past, as that is protected information under the ADA and until you have made a firm job offer to the candidate, you may not ask about disabilities.
Here is a good guideline article as regards ***** ***** can ask and what you should not ask about: http://bnrllp.com/guidelines-when-asking-job-applicants-about-drug-and-alcohol-use/
If the employee will not be driving a vehicle as part of their job, then you may choose to omit an discussion of the conviction in the interview process.
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I wish you and yours well in 2017,