An affidavit must be notarized, but need not be witnessed under this statute. A jurat is the bottom part of an affidavit where the officer certifies that the document was "sworn" before him. Jurat notarizations are required for transactions where the signer must attest to the content of the document, such as all affidavits.
Please see the following CA statute below:
3198. The original contractor shall serve upon the public entity an
affidavit and a copy thereof alleging the legal grounds upon which
he bases his claim and the facts in support thereof, and demanding
the release of all or such portion of such money or bonds as is
alleged to be withheld improperly or in an excessive amount. Such
affidavit shall also state the address of the original contractor
within this state for the purpose of permitting service by mail upon
him of any notice or legal document.