If the borrowing resolution so provides, any county treasurer may enter into a contract for the registration of notes with a bank or trust company having trust powers which may include provisions governing the issuance, reissuance, transfer, or exchange of notes on behalf of the county by the bank or trust company. Where a treasurer pursuant to such a contract delivers an original note or notes for such issue to a bank or trust company acting as a depository trustee with the understanding that the depository trustee will make appropriate book entries showing the holders of such notes, the bank or trustee by authentication shall, notwithstanding section 87c, be empowered to issue fully registered notes to the owners thereof on behalf of the treasurer without placing the actual or facsimile seal or signature of the treasurer thereon. A bank or trust company acting as registrar or depository trustee may authenticate notes by facsimile signature of an authorized officer or employee of the bank or trust company.