The police report will continue to exist.
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It will depend on what state you were tried in. In some states, including the state where I primarily practice, if a case is dismissed, then the defendant can move to expunge (purge, erase, remove) the records from that case from the public record. This would include removing from the public record arrest records, fingerprint records, and other records related to that criminal case. Check with an attorney in your area to see what the law in your state might be. If you have an expungement statute in your state, then you should move to expunge the records.