Neb. Rev. Stat. § 46-164

The board of directors, to whom such petition is presented, may require as a condition precedent to the granting of the same, that the petitioners shall severally pay to such district such respective sums, as nearly as the same can be estimated, the several amounts to be determined by the board, as such petitioners or their grantors would have been required to pay to such district as assessments had such lands been included in such district at the time the same was originally formed.