Where the district has not elected to transfer the duties of collector to the county tax collector, the county assessor shall furnish the district a duplicate of the applicable portions of the county’s assessment rolls at the time of transmittal of the statement of values required by Section 26627 and, upon receipt, a duplicate statement of the assessed values of all lands within the district subject to assessment by the State Board of Equalization. The rolls and statement so delivered shall for all purposes become the assessment rolls of the district.