Excuse my posting to this group, but it pertains to trees!

A neighbor tells me that one of my live oaks has dead branches that are
overhanging his property and I need to get them trimmed. Do I
understand properly that this trimming is his responsibilty, and not
mine? With all due respect to him, I have no problems with someone
getting such branches cut off my tree, but I would rather not pay money
to protect his property (a backyard shed). He seems to feel that this
maintenance is definitely up to me. I've always understood the reverse
to be true.

I don't want to turn this into a legal case, and neighborliness is
another matter, but if there is Austin city code that applies, I'd very
much like to be aware of it.

Thanks