(a) Whenever a Party nomination for a public office to be filled at a general or special election is not made at a primary election or by judicial
nominating convention, or when no valid designating
petition is filed with the board of elections (1) such nomination shall be made by the Executive Committee if for a public office to be filled by the voters of a political subdivision whose boundaries are coterminous with the County of New York or the Borough of Manhattan, and any vacancy in a nomination so made shall be filled by the Executive Committee or a subcommittee appointed by the Executive Committee for that purpose, and (2) such nomination shall be made by the appropriate District Committee if for a public office to be filled by the voters of a political subdivision wholly or partly
contained within, but embracing only a part of, the County of New York or Borough of Manhattan, and any vacancy in a nomination so made shall be filled by a subcommittee appointed by said District Committee for that purpose.