Final answer:
The only document that does not play a role in New Mexico's government is the statutes of neighboring states, as they have no authority in New Mexico. Hence, the correct answer is option (C).
Step-by-step explanation:
All of the documents listed play a role in New Mexico's government except the neighboring states' statutes. The United States Constitution plays a pivotal role by outlining the federal structure and establishing the supremacy clause that governs the relationship between state and federal law. The New Mexico Constitution is the fundamental legal document of the state, structuring the government and delineating its powers.
On the other hand, the New Mexico state statutes are laws specific to New Mexico that have been enacted by the state legislature. In contrast, the statutes of neighboring states have no direct authority or role in the operation of New Mexico's government.