No. A principal advantage to use of a limited liability company as a business organization is the flexibility of organization and management afforded under the relatively recent statutes (the Beverly-Killea Act) authorizing them in California. The founders decide how they want to manage the company (within limits). The statute calls for them to have a contract between them, known as the "Operating Agreement" that covers management and control, capital investment, and things of that sort. At formation, the LLC files a Form LLC-1 indicating who the initial members are, and whether the LLC will be managed by some of the members, all of the members, or non-member managers (as I recall the form, anyway).

An LLC can have a board of directors, and the board can be vested with real powers or simply serve as an advisory panel, but it is not required to have one and in fact I think it would be rather unusual.

LLCs rarely if ever issue stock, and thus are certainly not required to issue stock certificates. Even corporations that have outstanding stock do not always prepare and issue fancy pieces of paper as evidence of stock ownership. They must, hover, maintain a record of stock ownership.

Footnote: I have done research twice on whether an LLC can issue securities resembling corporate stock in that the security represents a share of equity ownership in the LLC and can be bought and sold like stock. The first time was six or eight years ago, and I think I concluded that, while very unusual, an LLC cound indeed issue a security representing a share of equity interest (but not membership) that could be transferred. Then, I researched the subject again a couple of weeks ago and could find nothing either authorizing or forbidding such an LLC security. If anyone who reads this answer can provide me with RELIABLE authority on this question, from any state, I'd be pleased to get a lead on it!