It shall be the duty of the Treasurer of State:
(1) To receive and keep all the moneys of the state not expressly required by law to be kept by some other person;
(2) To disburse the public moneys upon warrants drawn upon the State Treasury according to law and not otherwise;
(3) To keep a just, true, and comprehensive account of all moneys received and disbursed by him or her in books to be kept for that purpose, in which he or she shall state from whom moneys have been received and on what account and to whom and on what account disbursed;
(4) To keep a just and true account of each head of appropriation made by law and the disbursements under them;
(5) To render his or her accounts to the Auditor of State for settlement quarterly; and
(6) To perform all other duties which may be required of him or her by law.