Not necessarily. Usually when charges are pressed against someone it is up to the District Attorney to decide if the charges will be dropped before the case gets to trial. Just because the person who may have initially pursued pressing charges against someone has changed their mind it is unlikely charges will be dropped solely for this reason. The case is likely to be evaluated further to try to find out why the person who pressed the charge to begin with wants to drop it and why charges were filed in the first place.
In most cases it is the police who respond to a call requesting assistance and decide to make an arrest. Once the police make an arrest they will get a warrant for arrest. If the police make an arrest it is based on probable cause the police had and charges are unlikely to be dropped just because the person who initially made the call does not want to press charges. The case is very likely to continue on to trial and at the point it will be up to a judge to decide what will happen with the case.
So even if the person who initially wanted to charge you has changed their mind it does not mean you are off the hook.