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Generally - you are not exempt from unemployment tax, but you may request exemption from SDI.
For Unemployment Insurance (UI), Employment Training Tax (ETT), and State Disability Insurance* (SDI) purposes, employee includes an officer of a corporation, an employee under the usual common law rules, and any worker whose services are specifically covered by law.
Under the California Unemployment Insurance Code - certain employees and certain types of work
are not subject to one or more employment taxes: Unemployment Insurance (UI), Employment Training Tax
(ETT), State Disability Insurance (SDI) – please see more common exemptions in this publication - http://www.edd.ca.gov/pdf_pub_ctr/de231ee.pdf
See also the table starting from the page 16 in California Employer’s Guide - http://www.edd.ca.gov/pdf_pub_ctr/de44.pdf
The corporation must report your wages and pay contributions for unemployment insurance unless your corporation is not subject to the Federal Unemployment Tax Act (FUTA). Only certain types of nonprofit and agricultural corporations are not subject to FUTA.
In a private corporation, any person who is a corporate officer and sole shareholder, or the only shareholder other than his or her spouse, may file a statement electing to be excluded only from state disability insurance coverage SDI for contributions and benefits. Here is a form to use - http://www.edd.ca.gov/pdf_pub_ctr/de459.pdf