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The answer would depend on if there was any intent to defraud the bank by continuing to write the checks. If you were aware of the balance on the account and continued to write the checks, intent could be imputed and you could potentially be charged with check fraud and theft by deception.
The payee would also be able to file criminal charges for theft by deception because the person writing the check knew it was bad.
Fraud is generally defined in the law as an intentional misrepresentation of material existing fact made by one person to another with knowledge of its falsity and for the purpose of inducing the other person to act, and upon which the other person relies with resulting injury or damage.
So when the person knew there was no money in the account and continued to write checks that induced the payee to act, they definitely fall under the class of intentional fraud.
So yes, both parties could file criminal charges.