As a self-perpetuating board with no voting members, must we hold an annual meeting?

To answer that question, first be sure to see what your bylaws say. Bylaws typically have provisions about meetings. If your bylaws call for an annual meeting, you have your answer.

The exact phrase “annual meeting” does not appear in the California Corporation Code for public benefit corporations. However, there is a specific, relevant requirement in Section 5510: “A regular meeting of members shall be held on a date, time, and with the frequency stated in or fixed in accordance with the bylaws, but in any event in each year in which directors are to be elected at that meeting for the purpose of conducting such election, and to transact any other proper business which may be brought before the meeting.” CA Corp Code 5510

If a board meets regularly, you could simply designate one of those meetings as your annual meeting. Unless your bylaws say otherwise, It does not need to be a separate meeting in addition to your regular meeting schedule.

That said, why not have an annual meeting? It can serve a number of useful purposes! Check out:

Requirements for Nonprofit Annual Meetings | Nolo

How to Plan an Effective Annual Meeting for Your Non-Profit