If you are an immigrant seeking employment in California, your future employer must verify that you are eligible to work in the U.S. According to United States Citizenship and Immigration Services, this process involves the Employment Eligibility Verification Form, or I-9, which you and your employer must fill out after you have accepted the job. Your responsibility is only to provide the information requested on the first page.
There are instances where the form is not necessary. For example, a person who wants to hire you to work in a private home may not need to make it available if the job does not involve consistent hours or is sporadic in nature. As an independent contractor, you would also not need to fill out the form. If you have been working for the company since before November of 1986, you would not be expected to complete the information, or if the labor you are doing is not physically conducted in the United States.
You do not have to fill in the fields for telephone number or email address unless you wish to do so. While the employer is not allowed to ask you for a document that includes your Social Security number, you may have to provide the number if the employer is using the E-Verify system to check for employment eligibility. This information about USCIS form I-9 requirements is provided for your education. There may be other considerations or facets of the document that apply to you, so this should not be interpreted as legal advice.