1. The State Controller shall:
(a) Audit all claims against the State, for the payment of which an appropriation or authorization has been made but of which the amount has not been definitely fixed by law, which have been examined and passed upon by the State Board of Examiners, or which have been presented to the Board and not examined and passed upon by it within 30 days from their presentation.
(b) Allow of those claims mentioned in paragraph (a) as not having been passed upon by the State Board of Examiners within 30 days after presentation the whole, or such portion thereof as the State Controller deems just and legal, and of claims examined and passed upon by the State Board of Examiners, such an amount as the State Controller decrees just and legal not exceeding the amount allowed by the Board.
2. No claim for services rendered or advances made to the State or any officer thereof may be audited or allowed unless the services or advancement have been specially authorized by law and an appropriation or authorization made for its payment.
3. For the purpose of satisfying himself or herself of the justness and legality of any claim, the State Controller may examine witnesses under oath and receive and consider documentary evidence in addition to that furnished him or her by the State Board of Examiners. The State Controller shall draw warrants on the State Treasurer for such amounts as the State Controller allows of claims of the character described in this section, and also for all claims of which the amount has been definitely fixed by law and for the payment of which an appropriation or authorization has been made.