Hmmm. I guess it all depends on how many times this occurred. If it was a single, one-time incident, with no priors to the incident, I think you might be good to go. Below, I will paste all the DUI-related stipulations, highlighting what I think keeps you in the clear:
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"12. Have not been convicted of one of the following misdemeanors in the 8 years immediately preceding the date of application:"
- Operating while intoxicated, second offense, MCL 257.625(9)(b)
- Drunk driving, commercial vehicle, MCL 257.625m(4)
- Driving while license suspended or revoked, second or subsequent offense, MCL 257.904
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Now, there is another list of penal codes specifically written for offenses committed within the past three years, but I'm taking your word that you're good to go, so that list should be irrelevant.
Hope this helps.