In NJ, the expungement process is controlled by the statutory provisions of the criminal code. In essence whether you can get an arrest record (or a conviction record) expunged, depends on a number of issues, such as:
1. Was the charge dismissed without conviction.
2. Was a diversionary program like 'Conditional Discharge' used to get the dismissal.
3. If there was a conviction, what was the gradation of the charge you were convicted of (Crime/Ordinance, etc).
4. Whether the sentence imposed was completed.
There are other considerations, but the main issue is what happened to the charge? Assuming you meet the conditions for granting the expungement, in NJ it is requested via the filing of a formal petition to the Court. Once the expungement petition is granted, all records, including fingerprint records are placed in a secured storage facility. The records are not destroyed, they are secured to limit access, which is limited to certain statutory uses or by further order of the Court.
As to the last question, a police chief does not have the authority to throw out an arrest. Once a criminal charge has been filed, only the prosecutor can recommend the dismissal, and only the court can grant the dismissal.
I strongly urge you to contact an experienced criminal defense lawyer in your State to obtain appropriate legal counseling on these issues.