Legal Question in Family Law in California

Yes the burden of proof is initially on the plaintiff, but once the plaintiff presents a prima facie case, which their own testimony is enough to do, then the burden shifts to the respondent to present contrary evidence. If both sides present conflicting evidence, then the judge must weigh the evidence for both probative value (how persuasive it is) and credibility, and then make a determination based on the "preponderance of the evidence," which is lawyer-speak for deciding whether what the plaintiffs claim is more likely than not to be true and valid.