The simple answer: No. California law does not require that you give an employee a reason why they're being terminated; it is part of the "at-will" policy in California.
Indeed, the "Notice to Employee as to Change in Relationship" that is required by the Employment Development Department does not have a mandatory section for an employer to note why it is terminating an employee.
If you do give a reason, however, it is imperative that it is the truth and the real reason. If your termination is challenged (i.e., a wrongful termination lawsuit), you don’t want to be “back pedaling” and changing your story.
There are different schools of thought as to how to handle a termination. Many employers prefer to simply tell the employee, "This isn't working out," and not enter into an elaborate discussion with the individual.
Other employers prefer to explain to the person the reason behind the termination. There is no right or wrong way to handle this situation—it may depend on the person being terminated. Some individuals want to argue the decision, and that is probably when it's best to stay simple and explain it isn’t a topic for a discussion, but it is a decision that has been made. Other individuals may benefit from a simple discussion of why they are being let go and accept it as closure.
It's also best not to call a termination a "layoff" when it's truly a termination. If the position is filled relatively quickly, the ex-employee might find out and claim the layoff was a subterfuge and the termination was discriminatory in nature.
If an employer follows the progressive disciplinary path, most employees will know why they are being let go. If they receive oral warnings, followed by written warnings, and possibly even a suspension, there will be ample evidence supporting the decision to terminate in the event the decision is challenged.
A stated policy of progressive discipline tends to erode into the at-will relationship, since the courts have held that a promise of progressive discipline guarantees the employee ample warnings before termination. However, the practice of progressive discipline supports the employer.
If a termination of employment is a difficult decision to make, it is always wise to consult an employment law attorney to guide you through the process.