Every public utility or common carrier against which an assessment is made shall pay the amount thereof, and after such payment may under the conditions in this act provided, at any time within one year from the date the payment was made, sue the state in an action at law to recover the amount paid with legal interest thereon from the date of payment, upon the ground that said assessment was excessive, erroneous, unlawful or invalid in whole or in part. If it is finally determined in such action that any part of the assessment, for which payment was made was excessive, erroneous, unlawful or invalid, the state treasurer shall make a refund to the claimant as directed by the court.