See law on legality of public video recording in California.
Then, consider different cases of who took the video. If it was video recorded by police, that is a publicly owned body but what exactly ends up available for public review, in what format, and at what time is subject to department or state policy. If it was video lawfully taken by an individual, I suspect it might be handled like an individual's journal or intellectual property. It can be taken in as evidence but is only viewed by members of the court. In court proceeding records, the evidence (an exhibit) would only be named and described. This makes sense when you consider that a video may contain more information than is relevant to a case and it might still be intellectual property despite persons in it having no claim to expectation of privacy. It makes further sense when you consider that people often file lawsuits that are bogus just to test their luck. If all the evidence pulled for such lawsuits was free to view for the public, a bogus lawsuit could be used just to transfer a video from someone's personal computer to the public and lead to a cascade of suits.