A school-age person in the state shall have a right to a free public education as follows:
A. except for a school-age person who is detained in a state or local detention center or enrolled or residing in a state institution, other than a school-age person provided for in Subsection C of this section, a school-age person has a right to attend public school within the school district in which the school-age person resides;
B. except as provided in Subsection C of this section, a state or local detention center or state institution in which a school-age person is detained, enrolled or residing shall be responsible for providing educational services for the school-age person; and
C. a school-age person who is a client as defined in Section 43-1-3 NMSA 1978 in a state institution under the authority of the secretary of human services shall have a right to attend public school in the school district in which the institution in which the school-age person is a client is located if the school-age person has been recommended for placement in a public school:
(1) by the educational appraisal and review committee of the school district in which the institution is located; or
(2) as a result of the appeal process as provided in the special education rules of the department.