The Americans targeted officers at least once. A sniper at Saratoga, armed with a rifle and lodged in a tree, shot British officers and was instrumental in the American victory. The sniper is reportedly named Timothy Murphy.
This is an excerpt from the Wikipedia article:
"Morgan called on Murphy and said: "That gallant officer is General Fraser. I admire him, but it is necessary that he should die, do your duty." Murphy climbed a nearby tree, took careful aim at the extreme distance of 300 yards, and fired four times. The first shot was a close miss, the second grazed the General's horse, and with the third, Fraser tumbled from his horse, shot through the stomach. General Fraser died that night. British Senior officer Sir Francis Clerke, General Burgoyne's chief aide-de-camp, galloped onto the field with a message. Murphy's fourth shot killed him instantly."