Check your California Dept of Justice criminal history report ("Live Scan") by ordering a current copy at any of thousands of outlets throughout the state. That is fast, cheap and reliable. What is on your Live Scan will stay there and will be reported and visible to any California State licensing agency including the nursing agencies (BRN and BVNPT), unless you succeed in an effort to obtain an Order of Factual Innocence (unlikely on these facts). California State licensing agencies will require disclosure and an explanation of any improper conduct reported in criminal history reports, but a single theft incident not leading to conviction will not usually cause denial of a California nursing license.
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Probably not. Expungement is limited to cases that are dismissed or where you win at trial. And then you will probably have to file a motion for a finding of factual innocence, which the DA can oppose. If you plea but the charges are dismissed, that is the best you can hope for. In Sacramento, you can go online at www.saccourt.ca.gov and click on search case index to check and see if your case comes up.