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A dismissal would still show up in any background check. The record would show that you were charged with the crime and the disposition as a dismissal. Specifically, the following information is provided by Alabama: he Alabama criminal history record information maintained by the Alabama Criminal Justice Information Center (ACJIC)—often referred to as an Alabama criminal background check or a “rap sheet”—is a listing of certain information taken from records retained in connection with arrests made by Alabama’s local or state law enforcement agencies. Information submitted to ACJIC by Alabama law enforcement and criminal justice agencies, such as the name of the agency that submitted arrest fingerprints, the date of the arrest, the arrest charge, and the disposition of the arrest, may be included in ACJIC’s Alabama criminal history records check. This data is obtained from arrest fingerprint submissions, disposition reports, and other information submitted by agencies having criminal justice responsibilities. This information is maintained by the ACJIC, the official Alabama criminal history repository and the criminal justice agency responsible for connecting Alabama’s local, state and federal law enforcement agencies to the Federal Bureau of Investigation’s National Crime Information Center (NCIC).
And unfortunately, as of right now, Alabama does not have an expungement law. Normally, if the case is dismissed, you can get the criminal record of the charge removed from your records. However, Alabama does not offer this process.
The standard criminal background check only goes back a certain time period into the criminal history; however, fingerprinting will go back through the individual's entire criminal history based on their fingerprints. Did your unlawful possession happen a longer time ago such that it might not have shown up on the background checks?
The only other explanation why it isn't showing up on the background check is because it wasn't a reportable offense, only certain offenses are reported to the databases maintained. You can request a copy of your records from the FBI, which is the database checked for fingerprinting.
The instructions can be found here: http://www.fbi.gov/about-us/cjis/criminal-history-summary-checks
There would be a good chance it would not show up on your fingerprint check; however, you can make certain by submitting a request to the FBI