Who falsely accused you and made you sign a statement? While it is important that you tell the truth about this issue in order to exhibit good moral character, I don't necessarily see where you can mention it on the application if law enforcement wasn't involved. You could mention it during the interview, but make sure you bring a letter from the police department where the store is located to show that they do not have any records of an incident report or arrest.
Always, always, always tell the truth, the whole truth, and nothing but the truth on all forms.
www.capriotti.com -- firstname.lastname@example.org -- Senior Legal Counsel -- Capriotti International Law -- Legal disclaimer: This answer is offered for informational purposes only. It does not constitute an attorney-client relationship. Contact the American Immigration Lawyers Association www.aila.org for a referral to an experienced immigration attorney.
You will seriously prejudice your case if you are not truthful with USCIS. Never lie. Never assume anything. If you were arrested, say you were arrested. If your were not, then you were not arrested.
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