The Confederacy rarely ventured into true "Northern" territory. Even their "invasions of the North" often were into border slave states like Kentucky, Maryland, or Missouri, which contributed troops to both sides, rather than true Northern states.

When Lee invaded Maryland in 1862, he hoped to rally any pro-Southern supporters to his banners; however, most secessionists lived in eastern Maryland, while he invaded western Maryland, which tended more pro-Union. Especially under Lee's supervision, the Confederate soldiers were kept in good order and discipline. Antietam: The Soldiers' Battle by John Michael Priest gives a rare anecdote of an angry General Lee chewing out a soldier for stealing apples from an orchard.

Much the same occurred in 1863, when Lee made it into Pennsylvania for the Battle of Gettysburg. Typically, homes might be used as headquarters, and goods such as food and shoes might be "requisitioned" and paid for with worthless Confederate money, but looting and violent crime were apparently rare - I have read many, many books on the Civil War and I haven't found an instance of rape or outright murder on either of Lee's invasions of the North.

However, not every Confederate commander was Lee. When General Early entered Maryland in 1864, he sent a cavalry force under Brigadier General John McCausland to extort money from Northern towns. McCausland burned part of Chambersburg, Pennsylvania when they failed to pay the ransom of $500,000 in dollars or $100,000 in gold.

John Morgan's raid into Ohio in 1863 burned a bunch of property and confiscated not only public/military supplies but private goods as well. As far as I'm aware they harmed no civilians outright, and the raid was eventually boxed in and destroyed.

This was generally the rule with regular Confederate forces. Not so much with irregulars. The vengeance raids across the Kansas-Missouri border were particularly bad; one of the raids by Quantrill's band into Lawrence, Kansas basically massacred most of the men in the town. The exact details are debated, but what is known is that a lot of unarmed people were executed.

In short, Confederate forces never occupied any Northern towns for very long, and were usually driven out quickly. The exception was west of the Mississippi where the borders were more fluid. If you're interested in further reading on THAT, the Time-Life Civil War series can be found in most libraries, and one of the volumes, "Spies, Scouts, and Raiders" should delve further into the likes of Quantrill and his ilk.