Montana was a region on the North American continent on Earth.
During World War III, Montana was the location of several Titan II nuclear missile silos for the United States of America.
On April 5th, 2063, Zefram Cochrane launched the Phoenix, mankind's first warp-capable space ship, from a missile complex near Bozeman in central Montana; this led to Humanity's First Contact with an alien species, the Vulcans. (Star Trek: First Contact; VOY: "Year of Hell", "Homestead"; ENT: "Broken Bow", "Desert Crossing")
Later, a statue was erected of Dr. Cochrane near this spot, with him pointing to the sky, looking to the future. (Star Trek: First Contact)
One of the movies seen in the motion picture library of the Enterprise (NX-01) in the year 2152 was a western film called Montana Ambush. (ENT: "Cogenitor")