Nothing is ever automatic. The police investigate the crime to determine whether there is probable cause for arrest, and those charges are then run by a DA to accept the charges. If accepted than the case will be presented to a Grand Jury to determine whether formal charges will be brought. If the victim wants charges dropped they can testify in the Grand Jury or they can fill out an affadavit requesting charges dropped and that will be presented to the Grand Jury.
In many cases, with this affadavit, the Grand Jury no bills the case, meaning that charges are essentially dropped. But all of this is just dealt with on a case by case basis. People are prosecuted and convicted of assaults all the time even with unwilling and uncooperative victims.