(b) The board of supervisors shall approve an estimate for each town in the county public welfare district and shall levy taxes in each such town for the amount of the approved estimate for such town. 2. The legislative body of a city forming part of a county public welfare district shall appropriate the amount it considers necessary for administration and public assistance and care in such city and shall cause taxes to be levied for the amount of such appropriation. Nothing contained in this section shall be construed to prevent the financing of any such expenditure, in whole or in part, pursuant to the local finance law. 3. The board of supervisors shall appropriate, in the manner provided by law, the amount it considers necessary for the ensuing fiscal year for the various forms of public assistance and care and administrative expenses in the county public welfare district and shall cause the necessary taxes to be levied therefor in the territory of the county public welfare district.