The procedure for filing a petition for a writ of habeas corpus is spelled out in the CPLR Article 70. The privilege of the writ of habeas corpus shall not be suspended, unless when in Cases of Rebellion or Invasion the public Safety may require it.Habeas Corpus, in the Federal Court, is a petition that claims that you are being detained against your US constitutional rights. This Chapter explains an important right—the writ of habeas corpus. Any federal court may grant a writ of habeas corpus to a petitioner who is within its jurisdiction. The "Great Writ" of habeas corpus is a fundamental right in the Constitution that protects against unlawful and indefinite imprisonment. This Chapter explains an important right—the writ of habeas corpus. Under this statute, federal courts have considered both constitutional claims and claims of statutory interpretation. Henry Cook Salisbury, appellant, filed a petition for a writ of habeas corpus seeking his release from the custody of T. Ralph Grimes, Sheriff of Fulton County. The "Great Writ" of habeas corpus is a fundamental right in the Constitution that protects against unlawful and indefinite imprisonment.