The role of the CEO will likely be defined in the Corporation's bylaws. The employment agreement between the CEO and the Corporation can (and should) expand upon the day-to-day activities of that individual as well.
Legal disclaimer: I am licensed to practice law in the state of Washington and the answer provided above is for general information purposes only and should not be relied on as specific legal advice. This answer does not form an attorney-client relationship. You should consult with an attorney of your choice to fully advise you about your legal rights and obligations.
The duties of the CEO are defined in the Bylaws or Operating Agreement and the CEO's employment contract.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
The corp docs such as the bylaws or operating agreement or even an employment agreement may delineate the requirements of the CEO, but in the vast majority of small businesses you will not have that level of specificity.
There are commercially accepted tasks that a CEO is typically responsible for. I strongly suggest that the company or the officer have a lawyer draft up a proper employment agreement and outline what those expectations are.
Most of us here, including myself, offer a free phone consult so you may want to take advantage of that.
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