Mo. Rev. Stat. § 58.550

If an inquest is held over the body of a minor, the parent or conservator of the minor is liable for the costs and expenses of burial. If the person over whose body an inquest is held has any estate, the cost and expenses of burial shall be paid out of his estate. If there is no estate nor person liable and able to pay the expenses, they shall be allowed by the county commission out of the county treasury.