The California Revised Uniform Limited Liability Company Act, Cal. Corp. Code § 17701.01 et seq., clearly authorizes the appointment of officers:

A written operating agreement may provide for the appointment of officers, including, but not limited to, a chairperson or a president, or both a chairperson and a president, a secretary, a chief financial officer, and any other officers with the titles, powers, and duties as shall be specified in the articles of organization or operating agreement or as determined by the managers or members. An officer may, but does not need to, be a member or manager of the limited liability company, and any number of offices may be held by the same person.

Cal. Corp. Code § 17704.07(u). The CARULLCA even makes provision for the method of the appointment of officers:

Officers, if any, shall be appointed in accordance with the written operating agreement or, if no such provision is made in the operating agreement, any officers shall be appointed by the managers and shall serve at the pleasure of the managers, subject to the rights, if any, of an officer under any contract of employment. 

Cal. Corp. Code § 17704.07(v). The use of the plural "managers" suggests that an individual manager does not have the authority. But if an individual manager lacks the authority, what vote is required? The statute is conspicuously silent on this question. Notably, the statute does not use the defined term "majority of the managers", which unless otherwise provided in the operating agreement, means more than 50% of the managers of the limited liability company. Cal. Corp. Code § 17701.02(l).

These questions can be easily avoided, by answering them in the operating agreement.