Unlikely. Sounds like they didn't cause an arrest.
The opinions rendered herein are based on general principles of law. Laws vary from jurisdiction to jurisdiction and there are often numerous factors which can render advice or an opinion inapplicable. You should NOT make any decisions about the handling of a legal matter without first directly consulting with an attorney about the particulars of your case.
If you haven't received notice to attend a hearing then you have no case against you so no need to report anything. Breath deep and relax. You caught a break this time.
For Fairness & Your Freedom because sometimes good people find themselves in unpleasant situations
The response above is not intended as legal advice since it’s impracticable to provide thorough, accurate advice based upon the query without additional details. It is highly recommended that one should seek advice from a criminal defense attorney licensed in your jurisdiction by setting up a confidential meeting. Moreover, this response does not constitute the creation of an attorney-client relationship since this message is not a confidential communication because it was posted on a public website, thereby publicly disclosing the information, which is another reason to setup a confidential meeting with an attorney.
If the police were not called on the date of the incident, it's highly unlikely they would be at this point. I think you dodged a bullet.
Without police involvement, there will not be anything on your background check. The civil demand that you paid similarly does not have anything to do with your criminal history or your credit history.
If you want to see exactly what's on your DOJ (Department of Justice) background regarding criminal cases, follow the link below for information on how to obtain your background check.
The above answer is for general information only and is based on the information you posted. Every case is fact dependent, so to get a thorough analysis of your situation, you will need to consult face to face with an attorney licensed to practice in the jurisdiction where the incident took place. Do not conclusively rely on any information posted online when deciding what to do about your case.