Can I be tried twice for the same dui?

Since it was dismissed, you were neither found guilty nor not guilty, therefore there is probable no "double jeopardy" argument. However, the trial court might have put in the journal entry that the charge was dismissed "with prejudice." A dismissal "with prejudice" is final, meaning the case is over. A dismissal "without prejudice" means the case can be refiled.

Even if the case is refiled though, the prosecutor could be out of "speedy trial time." When a prosecutor refiles the same charge, he cannot reset the speedy trial clock. Ohio's speedy trial statutes set out 90 days of time to try a first-degree misdemeanor. Any time that you were in jail might be "triple counted," i.e. three days are charged for every one day in jail on that charge.

You should ask an attorney to review the case to see if the charge was dismissed with prejudice, and if it wasn't, then you should ask your attorney if he can file a motion to dismiss for want of speedy trial, assuming more than 90 days have elapsed (when adding the days from the first filing and the days after the second filing.) If the motion is denied, you might have an issue for appeal.