The governing body or the town council of a participating town in which a district has been created pursuant to this chapter may advance funds or provide matching funds from money not otherwise specifically allocated or obligated. Such funds may be received or generated from whatever source, including general revenues, special fees and assessments, state allocations, and contributions from private sources to a local district to assist the local district to undertake the transportation improvements for which it was created. To assist the district with an approved transportation improvement, the Commonwealth Transportation Board may allocate to a district created pursuant to this chapter only funds allocated, pursuant to Article 5 (§ 33.2-351 et seq.) of Chapter 3, and subsection A of § 58.1-638, to the construction districts and localities in which such transportation district is located.