Will this DUI arrest still show up on a background check?

I have a two part question: I was arrested for a DUI a year ago. I did not receive a ticket and my license has yet to be suspended. My attorney has been working the case from the beginning and has been to court to file a motion but it appears there is no record of my arrest in the court docket - nothing came up. I have been to the DMV since and was able to attain a new driver's license. Secondly, will an arrest that has been thrown out before even going to court (within a week of the arrest my attorney called me and emailed me the papers showing it was thrown out) show up on a background check? I work as an engineer and our customer (a municipality in a different state) is performing a background check on the engineers who will be working on site.