Someone is making the claim that I stole his property (necklace and cds). He has no proof of this. Can he go to police and charge me? Should I be concerned?

He can go to the police and file a report. It will be up to the police to investigate and the DA or grandjury to charge you if they believe there is enough reason to believe this could be true.

I do like that part where you never said you did not do it, merely they could not prove it