Most of the trails within Jay B. Starkey Wilderness Park are singletrack, apart from the main paved trail passing through the heart of the property. Some of the trails intersect without being marked super well, so it's helpful to have your map handy on the trails.
The most popular singletrack trail in the park is probably the mountain bike trail. You can run on this trail, but make sure to keep your eyes and ears peeled and always give bikes the right of way.