(a) a local health officer shall be eligible for appointment as registrar of vital statistics; and,

(b) no licensed and registered funeral director, undertaker or embalmer engaged or employed in the business or practice of funeral directing, undertaking or embalming, and no other person engaged or employed in the business of funeral directing, undertaking or embalming shall be eligible for appointment as a registrar, deputy registrar or sub-registrar of vital statistics. 3. (a) In towns and villages the registrar or registrars of vital statistics shall be appointed by the town board and by the village board of trustees respectively; a local town clerk shall be eligible for appointment as registrar of his town and of any village wholly within said town in which he has an office, and a village clerk shall be eligible for appointment as a registrar of his village and of any town in which he resides.

(b) In the cities, unless otherwise provided by charter, the registrar or registrars of vital statistics shall be appointed by the mayor.

(c) In each primary registration district consisting of a state hospital, charitable or penal institution, the registrar shall be the director or person in charge of such institution, provided, however, that he shall receive no additional remuneration for acting as such registrar.

(d) In an area designated as a county or part-county registration district, the county commissioner of health or public health director shall be appointed by the board of supervisors as registrar of such county or part-county registration district. If there be no county commissioner of health or public health director, then the board of supervisors, with the approval of the commissioner, shall designate the registrar. When such appointment is made, the terms of office of registrars theretofore appointed within such county or part-county registration district shall thereupon terminate, and the county commissioner of health or public health director or registrar so designated shall be the registrar of the entire area embraced within such county or part-county registration district. 4. When a district is divided into two or more primary registration districts, the appointment of a registrar for each shall be made by the same appointing authority which had jurisdiction over the original district. 5. (a) When two or more primary registration districts are combined, the registrar for such combined district shall be appointed by the board or city council of those former primary registration districts having had an aggregate of one hundred or more births, deaths or fetal deaths in each of the two preceding calendar years, and which theretofore made the appointment of registrars of the original districts, except that;

(b) in a county registration district, the county commissioner of health or public health director, or if there be no county commissioner of health or public health director, the designee of the board of supervisors of such county shall be appointed as registrar for the area of his jurisdiction as provided in paragraph (d) of subdivision three of this section;

(c) where the combined primary registration districts have each registered less than an aggregate of one hundred births, deaths or fetal deaths in each of the two preceding calendar years the registrar of the combined districts, or of the districts forming a part-county registration district shall be appointed by the board of supervisors of such county.