If the court determines that the petitioners have complied with the requirements of sections 110A.01 to 110A.36, it shall make an immediate investigation of the proposed district and of its proposed works, systems, or plans and of the engineering and economic feasibility of the project. The court, in its discretion, may make an estimate of the cost of the investigation and require the petitioners to defray part or all of the estimated cost before proceeding with the investigation.