N.M. Stat. § 4-20-2
That the present organization of the county of Quay as to precincts, school districts, officials and otherwise shall be and become the organization of the new county of Washington; the county seat of the county of Washington shall be and remain at Tucumcari until changed according to law. All officials of Quay county who were duly elected at the last general election and who qualified as required by law and all appointive officials duly qualified shall be and remain the officials of Washington county, holding their respective offices for the time for which they were severally elected or appointed, and qualified, and they shall perform all of the duties relating to their respective offices in the county of Washington hereby created.
NMS § 4-20-2