If the complaining witness wants to “drop all charges,” will the case be dismissed?

Not necessarily. There are many reasons why the alleged victim or reporting party may have a change of heart. It may be that the report of crime (violence, theft, or other violation) may have been false or inaccurate. It may also be that the person is scared to proceed with a prosecution. The police and the prosecutor's office are aware of all the reasons, and do not just “drop charges” especially in domestic violence cases. They attempt to re-interview the reporting party to understand the reason behind the change of heart.