Not necessarily.  Once the police make an arrest and charges are formally filed, it’s no longer up to the person that made the original accusations against you as to whether the matter will proceed or not.  It is not uncommon for a prosecutor to attempt to proceed with a matter even though the complainant requests that the charges be dropped.  However, on many occasions, the prosecution will need that witness to prove their case beyond a reasonable doubt, so the fact that a witness is uncooperative and does not want to pursue the matter is very helpful and puts the defense in a posit of power and control.