The board of each county where the damaged property is located must order the awarded damages to be paid, less any assessment against the property, before the property is entered for construction of the drainage project. If a county or a municipality that is awarded damages requests it, the assessment may not be deducted. If there is an appeal, the damages may not be paid until the final determination. If it is not clear who is entitled to the damages, the board may pay the damages to the court administrator of the district court of the county. The court shall direct the court administrator, by order, to pay the parties entitled to the damages.