Vacancies in the classified service shall be filled either by transfer, promotion, appointment, reappointment or demotion.

Whenever a vacancy is to be filled by appointment, the appointing authority shall submit to the director a statement of the title of the position and, if requested by the director to do so, the duties of the position and desirable qualifications of the person to be appointed and a request that the director certify to him the names of persons eligible for appointment to the position. The director shall thereupon certify to the appointing authority the name of the 10 ranking eligibles from the most appropriate register and, if more than one vacancy is to be filled, the name of one additional eligible for each additional vacancy or all the names on the register if there are fewer than 10. Except that in the appointment of attorneys or legal research aides under this section by the Attorney General for appointment in the office of the Attorney General the director shall certify to the Attorney General the names of all eligibles who meet the minimum qualifications for the particular class of attorneys. The Attorney General may then appoint any person on the register of eligibles without regard to position on that register. If it should prove impossible to locate any of the persons so certified or should it become known to the director that any person is not willing to accept the position, the appointing authority may request that additional names be certified until 10 persons eligible and available for appointment have been certified. Within 10 days after such names are certified, the appointing authority shall appoint one of those whose names are certified to each vacancy which he is to fill; except, that, in the event that he has fewer than the authorized number of persons from which to make his selection, he may choose from the remaining certified names or if he has fewer than three persons from which to make his selection he may make a provisional appointment as provided by Section 36-26-18. In the event that there does not exist an employment register which the director deems to be appropriate for the class in which the position is established, he shall prepare such a register within a reasonable time after receipt of the request of the appointing authority that eligibles be certified. Whenever an eligible has been certified to and rejected by appointing authorities three times, the director may remove the name of such person from the employment register.