Have an attorney review both the written denial, and your overall circumstances with you. Before answering I would want to know more both about the exact grounds for denial, and about what you have done/been doing in the last three years.
My understanding iss that many offices have denied naturalization cases on the grounds that one DUI, though NOT considered a "Crime Involving Moral Turpitude" ("CIMT") which would automatically bar naturalization, is still proof of lack of Good Moral Character ("GMC") which is a REQUIREMENT for naturalization in the last five years before applying (hence the instruction to wait five years).
These decisions are generally acknowledged to be wrong on the law, as one DUI alone would not be viewed as evidence of lack of GMC absent more, and many hae been appealed. Still, showing a clean record since the original conviction would be critical.
Speak with an attorney..
Generally speaking, simple DUI is not a crime of moral turpitude so if properly addressed in a naturalization application it should not result in a denial. Thus, if the 2007 DUI is the only blemish during the required good moral character (GMC) period then you should still be eligible for naturalization. Unfortunately, USCIS adjudicators often employ the presumption that if you have any criminal activity during the GMC period you cannot show good moral character, which is not true. However, it is important to remember that the burden is on you, the applicant, to show that you are in fact, a person of good moral character.
You should meet with an immigration attorney who can review your previous denial and your criminal records and advise you as to whether it makes sense for you to reapply now or wait before filing a new naturalization application.
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