HOUSTON — The Republic of Texas is unlike any other volunteer organization in what used to be the Republic of Texas.

Its monthly meetings are called joint sessions of congress. Members have minted their own silver and gold currency and carry ID cards warning police officers they are diplomatic representatives of the nation of Texas. Its vice president, a retired telephone company worker, sent a letter in 2011 to the governor of Oklahoma, informing her that she faced indictment because her state’s counties and territories were “trespassing inside the geographical boundaries” of the nation.

Such letters have failed to convince the authorities of the group’s novel belief — that Texas never legally became part of the United States and remains a separate nation. As a result of that belief, the group claims it had a duty to form a government, with a state department and with a court system run in part by a chiropractor in the Houston suburb of Katy.