Mo. Rev. Stat. § 88.683

The cost of paving or macadamizing the squares and areas as formed by the crossing or meeting of streets and other highways, or parts thereof or connections therewith, shall be levied as a special assessment, and paid for as follows: Such area shall be divided into parts or portions by lines drawn lengthwise along the middle of each of said streets or highways so intersecting or meeting, and the cost of said parts or portion shall be levied as a special assessment against the block or square contiguous to each, and prorated against the lots or pieces of ground in such block or square abutting on the street improved.