Me. Rev. Stat. tit. 36, § 703

If any municipality does not choose assessors and is not a part of a primary assessing area, the members of the select board are the assessors, and each of them must be sworn as an assessor. A member of the select board who is an assessor pursuant to this paragraph may resign the position of assessor without resigning office as a member of the select board. The position of assessor must then be filled by appointment pursuant to Title 30‑A, section 2602, subsection 2.