(1) Except as provided in subsections (2) and (3) of this section and sections 37-1249 and 37-1250, every motorboat on the waters of this state shall be numbered and no person shall operate or give permission for the operation of any vessel on such waters unless the vessel is numbered in accordance with the State Boat Act or in accordance with the laws of another state if the commission has by regulation approved the numbering system of such state and unless the certificate of number awarded to such vessel is in full force and effect and the identifying number set forth in the certificate of number is displayed and legible on each side of the forward half of the vessel.

(2) The owner of each motorboat may operate or give permission for the operation of such vessel for thirty days from the date the vessel was acquired in anticipation of the vessel being numbered. A duly executed bill of sale, certificate of title, or other satisfactory evidence of the right of possession of the vessel as prescribed by the Department of Motor Vehicles must be available for inspection at all times from the operator of the vessel.

(3) The owner or his or her invitee who operates a personal watercraft on any body of water (a) which is entirely upon privately owned land owned by only one person or one family and, if leased, leased by only one person or one family, (b) which does not connect by any permanent or intermittent inflow or outflow with other water outside such land, and (c) which is not operated on a commercial basis for profit may operate any personal watercraft on such body of water without complying with subsection (1) of this section.