Before you go off and step on toes....... are you 100% certain where the property lines are? Did you go find the pins in the 4 corners of your property? If so....proceed, if not, either call a surveyor or go locate the pins yourself, then ask them to move their fence, if they won't, call the city, the city may very well tell you it is a civil matter, just FYI.
I just had a similar occurrence, the guy behind me put up a property fence against my chain link fence 12 or so years ago, they are odd, so I just said fuck it. But then his POS started leaning towards my house and putting pressure on my fence.
I had my property surveyed, found out he was 10" on my side of the line on one end and 12" on the other, my city told me it was civil, I asked if because it was on my property, was it considered mine, they told me yes, I then asked for a permit to have a recreational fire, they came out and told the fucker to move his fence. I think they saw through my plan.....