A tornado swept through Montana’s remote and sparsely populated north-eastern corner on Monday, killing two people and injuring a third, authorities said.

Don Simonsen of the National Weather Service in Glasgow said the tornado touched down west of Reserve in Sheridan County between 7-15 p.m and 7-45 p.m. before crossing into North Dakota, where it weakened.

There also was at least one tornado reported about 20 miles (30 kilometers) south of Flaxville in Daniels County, Mr. Simonsen said.

Two people on a ranch about 13 miles (21 kilometers) west of Reserve were killed when the tornado struck, said Sheridan County Coroner David Fulkerson. A third person on the ranch was injured and transported to a hospital in Plentywood.

A nurse who answered the phone at Sheridan Memorial Hospital said she could not release any information about the injured patient.

North-eastern Montana is part of the Hi-Line, with vast stretches of plains and rolling wheat fields just south of the Canadian border. The area where the tornado touched down was “extremely isolated,” Mr. Fulkerson said.

Sheridan County’s estimated population was just over 3,200 in 2008, according the U.S. Census Bureau

The Sheridan County Sheriff’s Office did not have any immediate information on damages caused by the tornado.

Tornadoes are relatively rare in Montana, although on June 20, a tornado tore apart the state’s largest indoor arena.

The June tornado touched down on top of the Rimrock Auto Arena in Billings, tearing off the roof and some siding and causing extensive damage to the interior. The arena was not in use at the time.

The tornado was the first large tornado to hit Billings in more than a half-century.

City officials said hundreds of households also suffered some damage, either from severe winds or hail that accompanied the twister.

James Kraft, Yellowstone County’s emergency coordinator, has said insurance is expected to cover most or all of the rebuilding costs caused by that tornado.

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