Section 185. Difference about improvements

When the town superintendent or
  the  officers  of  a  village  or  city  having  the  powers   of   town
  superintendents  therein,  shall desire to make a new or altered highway
  extending beyond the bounds of such town,  village  or  city,  a  better
  highway  than is usually made for a common highway, with a special grade
  or roadbed, drainage or improved plan, and are willing to bear the whole
  or a part of the expense thereof beyond such bounds, but cannot agree in
  regard  to  the  same,  upon  written  application  of  either  of   the
  superintendents  or  officers and notice to all parties interested, such
  court shall make an equitable adjustment of the matters, and may  direct
  that  in  consideration of the payment of such portion of the additional
  expense by the town, village or  city  that  desires  the  improved  and
  better  highway,  as  shall  be  equitable,  its  officers, contractors,
  servants and agents may go into such town, village or city, and make the
  grade and roadbed, and do whatever may be necessary and proper  for  the
  completion  of  such  better  highway, advancing the money to do it; the
  amount of damages to each owner or occupant  shall  be  ascertained  and
  determined  by  the  supreme court in accordance with the eminent domain
  procedure law, such court shall, on notice to  all  parties  interested,
  direct  that  the  amount of damages assessed each owner or occupant, if
  any and all such expenses be paid by each, any or  all  of  such  towns,
  villages  or  cities as shall be just and equitable, and the damages and
  expenses assessed and  allowed,  as  in  this  and  the  last  preceding
  sections,  shall  be  paid  and  collected  as  if  fixed  by  the  town
  superintendents of the towns, or the officers of such villages or cities
  having the powers of such superintendents.