Is there a Certificate of Innocence or Certificate of Acquittal if charges are dropped?

No.  You can obtain a Judgment Entry of Dismissal, or a Prosecutor's Motion to Dismiss and order granting the Motion.  You would only have a judgment of acquittal if found not guilty by trial.  Even when you win in trial, there is no such thing as a "Certificate of Innocence" because an acquittal just means the government couldn't prove the charges.  You could present a copy of the Constitution which says you are innocent until proven g