Section 16. The state treasurer shall pay over to the persons entitled thereto all amounts allowed to them for expenses or fees in criminal prosecutions, or allowed by the courts as rewards or compensations to prosecutors, which have been duly certified by the clerks, if demanded within three years after the allowance thereof; but he shall pay no such amounts to a clerk of a district court, until the clerk has rendered a written account of all fines received by him since his last return, and of all fees which have remained in his hands for one year after their allowance.