As cdwjava stated, the police may not have been able to obtain the information to exonerate you. As such they take what they have and turn it over to the prosecutor. If the prosecutor sought the info the info and was informed it was a personal account and failed to prosecute the charges, then the system worked.
So, were you interviewed by the police prior to your arrest? If so did you inform them it is a personal account? Was that included in their report (at least as a claim by you)?
So what sort of timeframe are you speaking of here?
how long after you resigned were you arrested? When was the complaint by your former employer filed? When was the nolle prosequi entered?