Your question and dates don't really explain what your question is; however, if it is a first-degree misdemeanor charge of domestic violence, the statute of limitations is two years. If it is a felony charge, then the statute of limitations is six years.
If someone allegedly committed first-degree misdemeanor on September 19, 2012, the statute of limitations would not run until September 19, 2014.
Domestic violence is a very serious offense -- not just because of potential fines, court costs, and incarceration, but also because a domestic violence conviction will "Brady disqualify" someone (they will never be allowed to own a firearm in the future) and many possible employment opportunities will be barred. A first-degree misdemeanor (or felony) domestic violence convictions cannot be sealed/expunged. This is very serious business, hiring an experienced criminal defense attorney should be the immediate priority of anyone charged with a domestic violence offense.
I agree with the first answer. While the person claiming domestic violence can initiate a complaint, the state of Ohio is who prosecutes the case through the local county prosecutor's office. The defendant will need to have his attorney obtain discovery to determine the basis of the charge to see if there is a basis to ask for dismissal.
If the person has already been convicted of domestic violence a new charge of the same would be enhanced to a felony of the 4th degree. In that case, the statute of limitations would be at least 6 years. It also makes it more likely a prosecutor would pursue the charge. DV charges are very rarely dismissed and the complaining witness's wishes for dismissal are not given much weight. Factoring in that this is probably a felony makes a dismissal even less likely.