The applicable waiting period is a matter of New Hampshire state law and this question should be reposted in the NH forum. You might want to call the clerk's office in the court that your NH DUI came out of, but know that clerk's usually are not lawyers an may not know the correct answer to your question.
In Massachusetts, if you plead guilty (as opposed to admitted to sufficient facts and given a CWOF, that was dismissed upon completion of probation), the waiting period before you can seal the conviction is currently 10 years for a misdemeanor. Note that the waiting period will shorten in May of 2012 to 5 years for a misdemeanor conviction. In Massachusetts, ff you admitted to sufficient facts, the matter was CWOF'ed (a non-conviction) and eventually dismissed, you could petition to seal the CORI in May of 2012, when the current prohibition on sealing a charge that was dismissed following a period of probation will be removed. Note that I am talking about sealing rather than expunging. People often use the two terms interchangeably, but they are actually two different legal concepts. Sealing make the CORI generally inaccessible but the underlying documents still exist, whereas expungement removes all traces of any underlying documents. Expungement is rarely granted in MA.
Good luck,
Dominic Pang (617-538-1127)
RSA 265-A:21(I) provides that a record for a DUI/DWI may not be annulled by the Court until 10 years after the date of the conviction. I have included a link to the form used to file a Petition to Annul Record below.