N.M. Stat. § 54-2A-116
Resignation of agent for service of process.
A. In order to resign as an agent for service of process of a limited partnership or
foreign limited partnership, the agent must deliver to the secretary of state for filing a
statement of resignation containing the name of the limited partnership or foreign limited
partnership.
B. After receiving a statement of resignation, the secretary of state shall file it and
mail a copy to the designated office of the limited partnership or foreign limited
partnership and mail another copy to the principal office if the address of the office
appears in the records of the secretary of state and is different from the address of the
designated office.
C. An agency for service of process is terminated on the thirty-first day after the
secretary of state files the statement of resignation.