There are several places claiming credit to be the place of the northernmost battle of the civil war and which one we settle on largely depends on what we accept as a "battle".
During a raid the confederate cavalryman John Hunt Morgan surrendered his force near Salineville Ohio, which some claim to be the northernmost battle deserving of the term.
Possibly a saver bet would probably be the skirmish at Sporting Hill near the outskirts of Harrisburg Pennsylvania (it was the farthest members of the Army of Northern Virginia ever got and unless I'm totally mistaken it is further north than Salineville).
However, there was one other action which is held to be the northernmost "battle" of the civil war though it is contested whether or not the event deserves to be called a battle. Confederate raiders from Canada (not wearing uniforms), with the approval of the confederate government, robbed a bank in Saint Albans / Vermont killing one citizen and wounding another while having one of the raiders mortally wounded in return. If one accepts this as a battle Saint Albans in Vermont would be the the northernmost "battlefield" of the Civil War.