Phyllis, I looked in Wikipedia and found that there was a Hillsborough Militia District: "The Hillsborough District militia was an administrative division of the North Carolina militia during the American Revolutionary War (1776–1783).
At the outbreak of the Revolutionary War, the newly formed North Carolina government divided the state into six military districts. These districts each comprised a number of counties surrounding a significant town. The six districts, which corresponded with old judicial organizations, were: Edenton, New Bern, Wilmington, Halifax, Salisbury, and Hillsborough. Later, two additional districts were added, further dividing the mountainous western part of the state. Within the Hillsborough District were the counties of Caswell, Chatham, Granville, Orange, Randolph, and Wake." Was this perhaps what you were looking for?