A vacancy in an elective city office during a term of office shall be filled, at the Council’s option, by one of the two following procedures:
(A) Appointment. By appointment following public notice by the remaining members of the Council within 40 days after the vacancy occurs, except that if the remaining members do not constitute a quorum of the full membership, or if a petition is filed requesting an election, the Council shall call a special election as provided by law; or
(Iowa Code § 372.13(2)(a))
(B) Election. By a special election held to fill the office for the remaining balance of the unexpired term as provided by law.
(Iowa Code § 372.13(2)(b))
(Iowa Code § 372.13(2)) (1999 Code, § 5.11)