Question: What city and county seat in South Dakota, was Crow Dog, a Brulé Lakota subchief, nephew of former principal chief Conquering Bear, and leaders that helped popularize the Ghost Dance tried and convicted for shooting and killing principal chief Chief Spotted Tail?

Context paragraphs:
Ex parte Crow Dog: Ex parte Crow Dog, 109 U.S. 556 (1883) , is a decision of the Supreme Court of the United States that followed the death of one member of a Native American tribe at the hands of another on reservation land.  Crow Dog was a member of the Brulé band of the Lakota Sioux.  On August 5, 1881 he shot and killed Spotted Tail, a Lakota chief; there are different accounts of the background to the killing.  The tribal council dealt with the incident according to Sioux tradition, and Crow Dog paid restitution to the dead man's family.  However, the U.S. authorities then prosecuted Crow Dog for murder in a federal court.  He was found guilty and sentenced to hang.  The Supreme Court held that unless authorized by Congress, federal courts had no jurisdiction to try cases where the offense had already been tried by the tribal council.  Crow Dog was therefore released.  This case was the first time in history that an Indian was held on trial for the murder of another Indian.  The case led to the Major Crimes Act in 1885, which placed some major crimes (initially seven, now 15) under federal jurisdiction if committed by an Indian against another Indian on a reservation or tribal land.  This case was the beginning of the plenary power legal doctrine that has been used in Indian case law to limit tribal sovereignty.

Crow Dog: Crow Dog (also Kȟaŋǧí Šúŋka; 1833 – 1912) was a Brulé Lakota subchief, born at Horse Stealing Creek, Montana Territory.  He was the nephew of former principal chief Conquering Bear, who was killed in 1854 in an incident which would be known as the Grattan massacre.  Crow Dog was one of the leaders who helped popularize the Ghost Dance.  On August 5, 1881, after a long simmering feud, Crow Dog shot and killed principal chief Chief Spotted Tail (who was also at the Grattan massacre), on the Rosebud Indian Reservation.  A grand jury was convened and he was tried and convicted in Dakota Territorial court in Deadwood, South Dakota, and sentenced to death which was to be carried out on January 14, 1884.  He was imprisoned in Deadwood pending the outcome of his appeals.  According to historian Dee Brown in his bestselling book, "Bury My Heart at Wounded Knee":

Big Mouth: Big Mouth (Lakota: Itȟáŋka) (born 1822–died October 29, 1869) was an Oglala-born leader of the Brulé Lakota, highly regarded by the Brulé for his bravery and aggressive military leadership.  He was one of the signers of the second Treaty of Fort Laramie in 1868 and remained a bitter opponent of further American settlement, ridiculing Spotted Tail and other Sioux leaders upon their return from a mission to Washington, D.C..  He was the first son of Old Chief Smoke (1774–1864) and his third wife, Burnt Her Woman.  His twin brother was Blue Horse.

Deadwood, South Dakota: Deadwood (Lakota: "Owáyasuta"; "To approve or confirm things") is a city in South Dakota, United States, and the county seat of Lawrence County.  It is named after the dead trees found in its gulch.  The population was 1,270 according to the 2010 census.  The entire city is a National Historic Landmark District, for its well-preserved Gold Rush-era architecture.

Conquering Bear: Matȟó Wayúhi ("Conquering Bear") (1800 – August 19, 1854) was a Brulé Lakota chief who signed the Fort Laramie Treaty (1851).  He was killed in 1854 when troops from Fort Laramie entered his encampment to arrest a Sioux who had shot a calf belonging to a Mormon emigrant.  All 30 troopers in the army detachment were annihilated, in what would be called the Grattan massacre or "the Mormon Cow War" according to Army Historian S.L.A. Marshall in his book "Crimsoned Prairie."  Little Thunder took over as chief after his death.

Lower Brule Indian Reservation: The Lower Brulé Indian Reservation is an Indian reservation that belongs to the Lower Brulé Lakota Tribe.  It is located on the west bank of the Missouri River in Lyman and Stanley Counties in central South Dakota in the United States.  It is adjacent to the Crow Creek Indian Reservation on the east bank of the river.  The "Kul Wicasa Oyate" (lower…men…nation), the Lower Brulé Sioux, are members of the Sicangu (Burnt Thigh), one of the bands of the Lakota Tribe.  Tribal headquarters is in Lower Brule.

Spotted Tail Gravesite: The gravesite of the Brulé Lakota chief Spotted Tail stands outside an Episcopal cemetery on the outskirts of Rosebud, South Dakota, the government center of the Rosebud Indian Reservation.  It is marked by a stone obelisk which is engraved "Spotted Tail", Chief of the Sioux (Born 1823, Died Aug. 5, 1881).  The plot is surrounded by a wrought iron fence.  It is significant as the only site associated with Spotted Tail's life.  Spotted Tail was chosen to lead the Brulé when they were first confined to the reservation, and was an influential figure in the tribal politics of the 1870's.  His gravesite was listed on the National Register of Historic Places in 1980.

Little Thunder: Wakíŋyaŋ Čík’ala ("Little Thunder") was a Brulé Lakota chief.  Little Thunder was born about 1820.  He took over as chief of the Brulé after the death of Conquering Bear in 1854.  Little Thunder died about 1879 on the Rosebud Indian Reservation of the Dakota Territory.

Major Crimes Act: The Major Crimes Act (U.S. Statutes at Large, 23:385) is a law passed by the United States Congress in 1885 as the final section of the Indian Appropriations Act of that year.  The law places certain crimes under federal jurisdiction if they are committed by a Native American in Native territory.  The law follows the 1817 General Crimes Act, which extended federal jurisdiction to crimes committed in Native territory but did not cover crimes committed by Native Americans against Native Americans.  The Major Crime Act therefore broadened federal jurisdiction in Native territory by extending it to some crimes committed by Native Americans against Native Americans.  The Major Crimes Act was passed by Congress in response to the Supreme Court of the United States's ruling in "Ex parte Crow Dog" (109 U.S. 556 (1883)) that overturned the federal court conviction of Brule Lakota sub-chief Crow Dog for the murder of principal chief Spotted Tail on the Rosebud Indian Reservation.

Little Hawk (Crazy Horse's brother): Little Hawk (1842-1871) is the younger half brother of the famous Oglala warrior Crazy Horse # 3 (1840- 1877).  He was the offspring of the remarriage of Worm, Crazy Horse's # 2 widowed father, to a pair of sisters of the Brulé Lakota chief Spotted Tail, Iron Between Horns and Kills Enemy.

Supporting paragraphs: Crow Dog Deadwood, South Dakota
Answer: Deadwood