Whether a criminal case wil be dropped depends on the individual facts of the case, the prosecutor you are dealing with, and whether you have competent defense counsel. Based upon your question, I suspect you have been charged with the crime of harassment by a "tab charge." It may be a "payable" fine (I don't know off the top of my head), which means you can resolve the issue by simply paying a fine at court administration. Call the courthouse in the county in which the ticket was received and they should be able to tell you whether it is payable and if so, the amount. If you do pay the ticket, it is like pleading guilty, and you automatically waive your right to a trial, etc. If not, you will need to make your court appearances or risk having a warrant issued. The court date should be on the ticket.
Please be aware that this opinion is being offered merely to assist you in speaking with an attorney. It should not be construed as a legal opinion or as forming an attorney-client relationship.