There are two possible bases for a legal obligation to cut the grass:First, many towns--and almost all HOAs, if you're in a community with one--have rules, regulations, ordinances, etc. about having to cut the grass, maintaining the property, etc. If your municipality or community has such rules, you have to obey them and the neighbor can look to have them enforced againist you.Second, even in the absence of the above, if the property becomes sufficiently ill kept and, possibly, a breeding ground for animals or unwanted vegetation, it's possible it would rise to the level of a "nuisance" which someone could bring a legal action to abate. It's usually a high threshold or bar for something to be considered a nuisance, but it is possible.