The police arrest report would not be available at the court where you went; instead you would need to go to the arresting agency and request the police report from them. The certified letter from the court indicating you do not have anything filed against is good; however, USCIS will want to see the police report and if you have any charges filed against you. Advise seek counsel who can do an FBI background check and also there are various things an attorney can do to check your record more broadly and see what, if anything, you have filed against you. Seek immigration counsel who has experience in criminal matters.
No attorney-client relationship is created or implied by this communication.
A certified court disposition is good, however further documents might be needed. The larger question is whether you are inadmissible to the U.S. A foreign national can be inadmissible (not eligible for I-485) if he has been convicted of, admitted to committing, or admitted to committing the essential elements of certain crimes. My colleague is correct in that you'd be best advised to speak to an immigration attorney experienced in criminal matters.
Kindly note that this posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Remember, this site is akin to an internet blog. Do not rely on information here to make important decisions in your life. Make an appointment to meet with a licensed attorney in his or her office (or via Skype or phone) to obtain competent personal and professional guidance.