The most likely cause of the dripping sap is aphids. Aphids favor many deciduous and evergreen trees. Aphids are a piercing, sucking insect that feed off the fluids in the leaves and tender stems. They secrete a sticky fluid called honeydew that is a by-product of the tree sap they consume. When the tree is heavily infested, the honeydew can coat the limbs, trunk, and anything underneath the tree. Often, a black, sooty mold will form where this honeydew is secreted. You may want to read the Ohio State Extension publication: Aphids on Trees and Shrubs HYG-2031-90.