February 29, 2012 12:52:35 AM PST
Here in Washington, your side of the fence is yours to do with as you will including painting it or hanging stuff off it. It doesn't matter who built the fence.
It depends on the laws where you live and your relationship with your neighbors, but they may not be able to prevent you from using it to support your trellis if you want to.
Rodney
This post was edited by rodneywt1180b at February 29, 2012 12:52:35 AM PST