It shouldn't show up... but it might.
Under California law, employers are only supposed to ask if you have been convicted of a crime, or if you have a pending case where you are out on bail or your own recognizance.
However, the private companies that do pre-employment background checks sometimes screw up, and the dismissed case might still be show up on the report to the employer.
Please understand that this is a general discussion of legal principles by a California lawyer and does not create an attorney/client relationship. It's impossible to give detailed, accurate advice based on a few sentences on a website (and you shouldn't provide too much specific information about your legal matter on a public forum like this site, anyway). You should always seek advice from an attorney licensed in your jurisdiction who can give you an informed opinion after reviewing all of the relevant information.
It is likely that the arrest will have been promptly reported to the State criminal history data-base, but the dismissal will be reported, too. Both State (DoJ) (Live Scan) and FBI records (drawn from State records) will ordinarily continue to report both the arrest and the dismissal.
California law limits what use employers can make of arrests not leading to conviction, but the law does not preclude or prevent reporting of the full history. In particular, present FBI policy is that state court orders (for criminal history records repair such as post-conviction (P.C. 1203.4) dismissals) do not limit the FBI's reporting practices. The FBI takes the position that state laws limiting the use of the info is sufficient and that the FBI cannot be compelled by state laws or state courts to scrub its data to reflect post-event reports. Presently, the FBI removes nothing from the data base from which criminal history reports are drawn.
There is an obvious intention and disharmony between the states and the federal government here, one that Congress or the U.S. Attorney General needs to address. There is no resolution in sight, however.
My responses to questions on Avvo are never intended as legal advice and must not be relied upon as legal advice. I give legal advice only in the course of an attorney-client relationship. Exchange of information through Avvo's Questions forum does not establish an attorney-client relationship with me. That relationship is established only by individual consultation and execution of a written agreement for legal services.