Article I, Section 10 of the Constitution: "No state shall, without the consent of Congress... engage in war, unless actually invaded, or in such imminent danger as will not admit of delay."

Technically, a state cannot declare war, per the Constitution. However, there have been cases where states utilized militia without the consent of the federal government. In 1835, Ohio and Michigan engaged in the "Toledo War" over a 450-plus square foot strip of land. After a period of saber rattling between opposing militia, forces fired upon one another, resulting in a fatality. The federal government interceded and conciliated the parties. See: https://web.archive.org/web/20060820132210/http://www.geo.msu.edu/geo333/toledo_war.html

The case that best fits the question was in 1861. South Carolina militia under the command of General P.T. Beauregard shelled federal troops stationed at Ft. Sumter in Charleston harbor. It was without a doubt an act of war by South Carolina against the USA. See: http://www.civilwar.org/battlefields/fort-sumter.html