Can former employer tell prospective employers about criminal complaint they filed with police?

I lost a customers cash payment and quit before i could be fired for it. i left a note saying to take the amount lost out of my last check. 2 days later i got a call from police saying they were investigating embezlment. my employer sent me an invoice billing me for 4 invoices that said "invoice deleted. cash missing'. 2 of them were dated after i no longer worked there. these accusations are false and even their own paperwork proves that it must be someone else doing that. I offered to pay for the cash i lost but they didnt take it out of my check. and now i am certain they are telling prospective employers about this unproven allegations preventing me from getting a job. can they do that?