Some offenses -- such as domestic violence or drug possession -- could not only result in denial or naturalization, they could get him deported.
Even if he wasn't convicted, the facts of the case could be used to deny citizenship.
It is important to discuss this matter with an immigration attorney. If he has already been convicted, his lawyer should have advised him of the immigration consequences. The United States Supreme Court recently ruled that criminal defense attorneys must give non-citizen clients accurate information about the potential immigration effects of a conviction; lawyers who don't know enough about immigration to answer these questions are not competent to represent non-citizens.
What the specific charge is matters. There are some misdemeanors that are deportable (or can have the consequence of denial of naturalization or exclusion from the US if you leave and seek reentry) and others that do not have the same consequences.
If this person has already been convicted in the past, I'd suggest consulting face to face with an immigration attorney. They're going to want to see all the paperwork on the case so they will know the exact charge.
If the case is pending, then you're going to need a criminal defense attorney.... and one that is familiar with immigration consequences.
And lastly, if you're a combination of the two - already convicted, but need to try and "fix" things for immigration purposes, then a criminal defense attorney with experience in post-conviction relief is who you're after. Depending on the advisement of rights, waivers and other specifics of your plea (assuming it was a plea, not a conviction after trial) may give you a way to withdraw the plea and vacate the judgment.
The only way to know the right questions to ask and therefore get the right answers is to consult an attorney face to face to discuss your situation.