While Putnam is still recognized as the "historic district", it was annexed by Zanesville in 1872. Putnam (originally called Springfield) was founded in 1801 by Dr. Increase Mathews, Levi Whipple, and Brig. Gen. Rufus Putnam. It was renamed Putnam in 1814. The Stone Academy was built by Mathews, Whipple and Buckingham in 1809. Whipple organized the abolitionist movement in Putnam according to the Muskingum histories. His barn was burned down because of his activities. A lot of fights over the slavery issue occurred between residents of Putnam and Zanesville!
Harriet Beecher Stowe's brother was also a minister of the Congregational Church in Putnam and very actively involved in this movement.
I've done some research trying to find out if Increase was involved - he had to have built that trap door in the Stone Academy - but I haven't been able to pinpoint anything definitive. I heard (when I toured his house that's now a museum?), or read somewhere, that the home he built for his son Henry was an underground stop. But I haven't been able to locate any reference.
Additionally, Increase's sister and brother-in-law, Susannah and Captain Jonathan Stone, and their son Col. John Stone were active abolitionists at Belpre in Washington County. I believe their home is also nationally recognized as an underground railroad stop.