If the proposed district is all in one county, the board of supervisors may pay all necessary preliminary expenses in connection with the district. If it extends into other counties, the boards of the respective counties may pay a proportion of the expenses as the work done or expenses created in each county bears to the whole amount of work done or expenses created. The amounts shall be ascertained and reported by the engineer in charge of the work and be approved by the respective boards which shall, as soon as paid, charge the amount to the district, as their interests may appear, as soon as the district is established. If the district is not established, the amounts shall be collected upon the bond or bonds of the petitioners.