Arizona law lets you ask a court to seal the records of a criminal case under Ariz. Stat. § 13-911. It covers an arrest with no charge filed, a dismissed charge, or a not-guilty verdict. It also covers a conviction, once you finish your sentence and wait the set time. Some offenses cannot be sealed. A second law, Ariz. Stat. § 36-2862, lets you ask a court to expunge the record of certain marijuana offenses. Both start with a petition. You can ask for a hearing.
If the court denies a sealing petition, you must wait three years to file again.
The marijuana law, Ariz. Stat. § 36-2862, is known as Proposition 207. It has its own petition, apart from sealing under Ariz. Stat. § 13-911.