Whenever, pursuant to the provisions of this chapter, the selectmen receive a petition to lay out roads over existing private rights-of-way or to lay out a class V highway over an existing class VI highway and such private right-of-way or class VI highway does not conform to construction standards and requirements currently in effect in the town, the selectmen may conditionally lay out roads upon compliance with betterment assessments as provided in this section and in N.H. Rev. Stat. § 231:29-33. Prior to commencement of conditional layout, however, a public hearing shall be held, written notice of which shall be given by the appropriate governing board to all owners of property abutting or served by the private right-of-way or class VI highway, at least 14 days before the hearing, at which hearing details of the proposed construction, reconstruction or repairs, and the estimated costs thereof shall be presented by the selectmen. Conditional layout proceedings may commence 10 days following the public hearing unless within that period a petition not to conditionally lay out said thoroughfare signed by a majority of the owners of property abutting or served by the existing private right-of-way or class VI highway is received by the selectmen. If a highway is so laid out, the selectmen may construct, reconstruct, repair or cause to be constructed, reconstructed or repaired such highways, streets, roads, or traveled ways to conform in every way with the highway or street construction standards and regulations previously established by the town. The betterment assessments shall be assessed under the provisions of N.H. Rev. Stat. § 231:29.