An N-400 citizenship application is the one used by U.S. green card holders to request U.S. citizenship via a process called naturalization. An entire section of the form (Section D) is devoted to "Good Moral Character." It asks various questions about whether you have ever committed any crimes; been arrested, cited, or detained; been charged with a crime; spent time in jail or prison; and so forth.
This raises the question of whether a traffic violation is a crime that needs to be mentioned on your N-400 citizenship application. The answer is not entirely clearcut.
In order to qualify to naturalize, you must meet certain requirements, such as having spent a specified amount of time continually residing and physically present in the United States (five years, for most people), having lived in the same U.S. state for at least three months previous to filing the application, being able to demonstrate literacy in English (reading, writing, and speaking), passing a test of your knowledge of U.S. history and government, understanding and obeying the U.S. constitution, demonstrating good moral character, particularly in the five years leading up to your application, and more. (You can demonstrate fewer years of good moral character if you fall into a category of green card holders that's allowed to apply earlier, such as spouses of U.S. citizens.)
For purposes of this article, the most important issue is your good moral character. (For a more complete list of criteria, see Who Is Eligible to Become a Naturalized U.S. Citizen)
Whether you can show good moral character depends in part on the judgment of the immigration officer considering your case. In general, to show good moral character, you must meet the standards of behavior in your community. Being a supportive family member, getting involved in community activities, performing responsibly at a job, and doing volunteer work are all signs of good moral character.
Committing crimes, of course, will weigh against your showing of good moral character. Certain crimes will automatically destroy your showing of good moral character, such as having committed an aggravated felony or genocide or torture, or any crime for which you were imprisoned for an aggregated period of 180 days or more. But it's unlikely that a traffic violation would put you into any of these categories.
More important in your situation is the exact nature of your violation, how many of them are on your record, and whether you took appropriate followup steps, such as paying your fines and perhaps enrolling in a remedial driving class after receiving a series of tickets. For example, a person who was ticketed for running through one four-way stop sign and immediately paid a fine will have a much easier time proving good moral character than someone who got three tickets in a row for running a stop sign, failed to pay the fines or attend traffic school, and was arrested as a result.
If your only tickets were for parking violations -- that is, things like staying too long at a parking meter or parking your car in a red zone -- you don't even need to mention these on Form N-400. But for any violation where you were behind the wheel, or your motor was running, your best bet is to mention it.
If you were cited for a relatively minor moving violation, your naturalization application still stands a good chance of success. You can also improve your chances by waiting longer to file Form N-400, so that you can show a longer stretch of time during which you received no traffic tickets. (Take the bus, if you have to!)
When in doubt about whether a violation is serious enough to mention, it's usually better to disclose it and then do your best to explain it to USCIS than to hide it and face the agency's suspicion that you aren't behaving honestly. Remember, you'll be submitting fingerprints as part of the application process, so anything that made it onto your criminal record will come to light whether you describe it on the N-400 or not.
You'd also be wise to consult with a knowledgeable immigration lawyer. Your lawyer will review your record and evaluate whether your previous traffic violations might have a negative impact on your petition, then help you develop a strategy for showing good moral character despite the traffic violations.
Your lawyer will probably recommend that you undergo a fingerprint check before submitting the N-400. If the results of the check, plus your own description of your traffic violations, shows a record that's especially negative, the lawyer may recommend that you not apply for citizenship at all, or that you wait some years before applying.