New Mexico Complaint for Writ of Habeas Corpus is a legal document used in the state of New Mexico to initiate a legal proceeding seeking relief for unlawful imprisonment or detention. This complaint is filed by an individual who claims that their incarceration or detention violates their constitutional rights, such as the right to due process or the right to be free from cruel and unusual punishment. Keywords: New Mexico, Complaint for Writ of Habeas Corpus, legal document, unlawful imprisonment, detention, relief, constitutional rights, due process, cruel and unusual punishment. There are several types of New Mexico Complaint for Writ of Habeas Corpus, depending on the specific circumstances and the relief sought: 1. Habeas Corpus ad Subjiciendum: This type of writ is used when the petitioner is currently in custody or detention and seeks an order from the court to determine the legality of their detention. 2. Habeas Corpus ad Prosequendum: This writ is utilized when the petitioner is already in custody or detention and wants to be temporarily released in order to face pending criminal charges in another jurisdiction. 3. Habeas Corpus ad Testificandum: This type of writ is filed when the petitioner is currently in custody and requests to be brought before a court as a witness in a legal proceeding. 4. Habeas Corpus ad Hacienda ET Recipient: This writ is employed when the petitioner is located in a different jurisdiction and needs to be transferred to another jurisdiction for trial or other legal proceedings. Each type of New Mexico Complaint for Writ of Habeas Corpus serves a unique purpose depending on the circumstances of the petitioner's detention and the relief they seek from the court. Keywords: Habeas Corpus ad Subjiciendum, Habeas Corpus ad Prosequendum, Habeas Corpus ad Testificandum, Habeas Corpus ad Hacienda ET Recipient, petitioner, custody, detention, relief, legality, jurisdiction.