Tulips do not do well in warm soil, so planting them too soon results in poor blooming the following spring. However, tulip bulbs must be planted before the soil freezes.
You should plant tulip bulbs between late August and the first hard freeze in your area. Much of Ohio falls in U.S. Department of Agriculture Plant Hardiness Zone 5, but Southern Ohio is actually in Zone 6 and has a slightly milder climate. You should plant tulips bulbs in Southern Ohio in mid-October, as suggested by Ohio State University Extension.
Planting tulips up to a depth of 12 inches keeps them cooler. Deeper planting may keep bulbs from multiplying through the years.