In this area, the term "charges dropped" means that someone was arrested and when they went to court the case was dismissed. If no one was arrested then there were no charges in the first place - there was an investigation.
If there is no physical evidence other than the statement of a child, the usual course of action is to see to whom was this incident disclosed? Did the child tell several different relatives or friends at different times, and were all versions of the story consistent? That might lend more weight to her story.
In Connecticut a minor victim of sexual assault would be interviewed by a forensic psychologist on the Multijurisdictional Investigative Team. They are only interviewed once to avoid retraumatizing them over and over.
Kids don't generally make up stuff like this on their own, however, I have seen parents coach their children to say things that weren't true, often in an attempt to gain leverage in divorce and/or custody proceedings.
Your best bet to find out what happened is to have the guardian of the child contact the police agency to which you originally complained.
Cogito ergo summopere periculosus.
Fiat justitia, ruat coelum.