(a) Except as otherwise provided herein, appointment or promotion to a position in the competitive class shall be made by the selection of a person on the appropriate eligible list willing to accept such appointment and whose final rating in the examination is equal to or higher than the rating of the third highest ranking eligible on the list indicating willingness to accept such appointment. The term ranking as used herein refers to the order in which the names of eligibles appear on the eligible list as provided in section 3.5 of this Title.

(b) Whenever a vacancy exists in a competitive class position and an open competitive examination does not result in an eligible list containing the names of at least three persons willing to accept appointment, the Civil Service Department may permit the appointing authority to nominate a person for noncompetitive examination for such position and, if such nominee shall be certified by the Civil Service Department as qualified, he may be appointed to fill such vacancy; or the Civil Service Department may designate the eligible list, if there be one, as a continuing eligible list in accordance with section 57 of the Civil Service Law, and insert therein the names of additional eligibles as they are found qualified by examinations held at such intervals as may be prescribed.

(c) Promotion by noncompetitive examination may also be made as provided by law.

(d) Certification of a promotion eligible list shall not be required for filling certain vacancies. A promotion eligible list shall not be certified for filling a permanent vacancy created by upward reclassification of a permanently encumbered position where promotion from such list would require the layoff of a permanent employee or the reassignment of a permanent employee to a different geographical location; but this provision shall not apply if the incumbent whose position was reclassified has, following such reclassification, twice failed to qualify for promotion to the reclassified position.

(e) An open competitive eligible list shall not be certified for filling a permanent vacancy created by upward reclassification of a permanently encumbered position if appointment from such list would require the lay-off of a permanent employee or the reassignment of a permanent employee to a different agency, to a different geographical location; but this provision shall not apply if the incumbent whose position was reclassified has, following such reclassification, twice failed to qualify for appointment to the reclassified position.