Completed pre-trial diversion and case was dismissed. Will this show up on background check and if so, how will it show up?

On normal background checks it will not show up at all. ( this is if they use the police background checks) The pubic version they give out only shows convictions.

On national security and police background checks it will show arrested, and dismissed by pretrial diversion.

Today with computers and PI's and more if someone hires someone to do a very detailed background on you, almost anything will show up.

It just all depend on who and how indept the background is going.
For example when I went to work for the Justice dept, they send investigators to talk to eveyrone I lived next to for 10 years, they talked to college teachers, high school teachers, that lead them to friends of mine during those years. They even knew lines I used to pick girls up in college,