Section 111. Payment and apportionment of cost among counties and towns

The
  board  of  supervisors  of  any  county,  in lieu of proceeding with the
  construction or improvement of a highway or highways under sections  one
  hundred  and  ninety-four  or  one hundred and ninety-five, or under the
  general or special law governing  the  construction  or  improvement  of
  highways,  may  appropriate  and  contribute  to the county road fund an
  amount to be applied to the construction or improvement,  reconstruction
  or  maintenance of such highway or highways under the provisions of this
  article. Such moneys may be raised by the county by tax  in  the  manner
  provided  in  such sections or other law with respect to moneys provided
  for the construction or improvement of a highway or highways  thereunder
  or  may  be raised pursuant to the local finance law; and the provisions
  of such section or laws authorizing apportionment of the expense or part
  thereof to the towns and prescribing the manner  of  such  apportionment
  and the method of providing the town's share thereof shall apply to such
  county contributions. Nothing herein contained, however, shall prevent a
  board of supervisors from providing such contribution to the county road
  fund  by general county tax, without apportionment of the expense to the
  towns.