You have described a criminal arrest that did not result in a criminal conviction as the state charges were rejected. Therefore you may apply for U.S. Citizenship however, the exact legal presentation of the case is crucial as even with an admission of a criminal act such as yours as you stated "I got arrested in 2011 for domestic battery for slapping my X-girlfriend's face" the interviewing officer may deny your naturalization for an act of moral turpitude.
You need to meet with a practicing immigration counsel in person in my opinion.
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On your application, you will want to disclose the arrest, and include the letter stating that no charges were filed against you. There may be other considerations before applying for citizenship, so it may be worthwhile to have an attorney guide you through the process. Many attorneys offer payment plans.
I suggest you consult an immigration attorney. You may find one by visiting www.aila.org. In your question you make statements that can be misconstrued , for example you state that you were arrested. Do you have an official court disposition/adjudication. You can file for citizenship because you meet the time requirements, however, you should consult an immigration attorney.
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