Connecticut is the official State tartan, adopted by the Connecticut legislature under Governor Rowland in 1995.

The large blue stripes represent Long Island Sound; the large green stripes symbolize Connecticut's forests, the medium gray stripes represent granite; the red and yellow pin stripes represent autumn leaves; and the white pin stripes are a symbol of winter snow.

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.

Source:

The State Tartan: CT.gov
Tartans of Scotland
Scottish Tartans Museum; History

Links:

Cultural Symbols - 50 states