Trespass Violation

What is the name of your state (only U.S. law)? New York

I was issued a summons for a trespass violation (14.05) that was subsequently dismissed. Can i truthfully answer, under the law, that I have not violated a United States law?

We can not tell. Can you truthfully tell us you weren't trespassing.
Now if they asked if you were CONVICTED of breaking the law, then no the dismissal would not count as a conviction.