The Carolina Tartan was recognized as the official tartan of the state of North Carolina in 1991. South Carolina also designates the Carolina tartan as state tartan.

Tartan refers to fabric woven into plaid patterns representing clans (families) or regions in Scotland.

In old Scotland, the tartan was used for clothing and as a banner or flag. Because a family or community worked the cloth together, their clothing was made of the same patterns, and so a person could be recognized by the Tartan plaid that he wore. Tartans can also be designed as a symbol commemorating a special event or person.

From Tartans of Scotland:

"The Carolina tartan is based on a fragment of a coat of the Royal Company of Archers dated c.1730, believed to be the same sett as was used for the wedding ribbons of Charles II in 1661. The tartan commemorates the historic link" (the Carolina colonies were named for Charles).

The Scottish Tartans World Register also has a North Carolina Tartan:

From North Carolina State Library:

"A unique blend of red, azure, black, yellow, green and white, the Carolina Tartan was first registered with the Scottish Tartans Society in 1981, and is also the Official Tartan for South Carolina. The design is a variation of a tartan associated with two monarchs--King Charles II, who gave his name to the Carolinas, and the honorary bodyguard of King George II, who designated both North and South Carolina as Royal Colonies in 1729. Large numbers of Scots helped to colonize the Carolinas in the 17th and 18th centuries, and the State is now home to a number of festivals, games, and organizations that celebrate Carolina's Scottish heritage, including the Flora MacDonald Highland Games, the Scottish Tartan Museum, and the North Carolina Scottish Heritage Society."

Source:

Tartans of Scotland
Scottish Tartans Museum; History
Tartans - Carolina: Destinations in Scotland

Links:

Cultural Symbols - 50 states