(a) If the boundaries of a local improvement district as petitioned for embrace a part of any lot, block, or parcel of land which, upon the county assessment books, is assessed as a whole, any signer of the petition may demand, in writing, of the county assessor that he shall apportion the assessment for state and county purposes upon the lot, block, or parcel of land so as to show the assessed value of that portion which is within the proposed district and the assessed value of the remainder which is without the district.
(b) It shall be the duty of the county assessor, within ten (10) days after the request is made of him, to make the reassessment and to deliver to the city or town clerk or recorder a certificate showing the assessed value of that portion of the lot, block, or parcel of land that is within the district, to the end that in determining whether a majority in value has signed the petition, the city or town council can compute the value of the portion of the lot, block, or parcel of land that is within the district.