Let me add a couple of things.
Most large civil service agencies have their own in house personnel who are pretty skilled at doing backgrounds. Smaller agencies often contract with retired police background investigators who are fairly thorough at what they do. It is rare that a government agency relies on a $29 internet background check to vet someone for a position of this importance.
Section 432.7 (a) of the Labor Code prohibits an employer from asking an applicant to disclose an arrest or detention that did not result in conviction. It also prohibits an employer from denying someone employment based solely on a record of arrest or detention that did not result in conviction. But the law only speaks to arrests and arrest records and not to the applicant’s conduct.
Friends, relatives, references and coworkers will invariably mention an arrest to the background investigator. Employers then legally bypass the prohibitions of Labor Code 432.7 (a) by obtaining information about the incident in question through their own, independent investigation into the matter. Any decision to hire or deny employment is then made based on the applicant’s conduct as determined by the independent background investigation and not through the applicant’s disclosure of an arrest, or review of arrest records.
Whether the applicant’s conduct meets the criteria for disqualification will vary from agency to agency. If it’s just a matter of the applicant being in the wrong place, at the wrong time and looking like someone else who was wanted and being mistakenly arrested, then it’s unlikely this will pose a problem. OTOH, if the applicant actually committed a crime but for whatever reason wasn’t convicted, he may have an uphill battle.
Many years ago I did a background on a rapist who was seeking a law enforcement position. Blood and semen on the suspect’s clothing established him as the perpetrator, however, without going into a lot of detail, the arresting agency bungled its handling and all of the physical evidence was thrown out. This reduced things to a he said/she said case and the jury acquitted him. While not guilty as a matter of law, he was still a rapist as a matter of fact and he failed the background for the position he was seeking.
Most government agencies require applicants to be of good moral character. Most also require that applicants possess general qualifications such as integrity, honesty, sobriety, dependability, industry, thoroughness, accuracy, good judgment, initiative, resourcefulness, courtesy, ability to work cooperatively with others, willingness and ability to assume the responsibilities and to conform to the conditions of work characteristic of the employment, and a state of health, consistent with the ability to perform the assigned duties of the class.
If an independent investigation of the circumstances surrounding the event that led to your arrest determines you lack any of the general qualifications established by the agency you are applying with, you may be facing a problem.

