The assessments levied on the lands shall be made in and by the court where the petition was filed and the proceeding is pending, as provided in part 8 of this chapter as to assessments where the district is wholly in one (1) county, such assessments to be made on the lands in all of the counties included within the district. The clerk of the county in which the petition is filed and the proceeding pending shall make out the drainage assessment book in which the assessment for the entire district appears. The clerk shall then copy so much of the drainage assessment book as contains the assessment of lands in any other county than that where the petition was filed and proceeding is pending, certify under seal that it is a correct copy of that portion, or part of such book, and transmit or deliver it, to the trustee of such other county, taking a clerk’s receipt for the copy.