Mo. Rev. Stat. § 431.100

If a claim against a county be for work and labor done, or material furnished in good faith by the claimant, under contract with the county authorities, or with any agent of the county lawfully authorized, the claimant, if he shall have fulfilled his contract, shall be entitled to recover the just value of such work, labor and material, though such authorities or agent may not, in making such contract, have pursued the form of proceedings prescribed by law.