If the summons was returnable on April 24 and the paperwork was not ready, you may have a speedy trial argument for dismissal. That would be the law if you had been given a Desk Appearance Ticket, where the speedy trial clock begins to tick on the day you appear in court pursuant to the D-A-T. I have not heard of this coming up in the context of a summons but the same argument can be made -- you were given a summons to appear on a certain date and you did but the paperwork was not ready and therefore the clock began to tick. You are charged with a violation, which has only a 30 day speedy trial clock.
The above is for informational purposes only and not meant as legal advice.
At 346 Broadway, the police officer prosecutes the summons and the judge is the one to offfer a plea bargain or preside over any trial. If you have an attorney, he can review the narrative on the back of the court's summons and determine whether there is any basis to move for dismissal.