How can I get my arrest record expunged from Washington DC park police?

Although I do not practice law in the District of Columbia, here are my initial impressions.  The general rule is that if a criminal charge has been dismissed, it has been erased/expunged from the public record.  You may want to contact the arresting police department with proof of the dismissal (which can be obtained from the court) to request that your police file (i.e. mugshot, fingerprints, etc.) is also erased.  However, the facts that you have provided are slightly contradictory -- if you were arrested, then you were, in fact charged with a crime.  Therefore, the first step in this process may be to clear any questions regarding the exact resolution of this matter.  Good luck.