how close to my property can my neighbor dump his grass clippings
Under general legal principles, as long as the clippings are on his property, they can be as close to your property as he likes: e.g. 1 millimeter from the property line. He can't dump them on your side, but he can put them anywhere on his own property. It's possible there is some local (e.g. municipal, or town/city) code (like a health or building code provision) which may govern this and require some "set back" (that the clippings not be within X feet of your property) or that he may have to dispose of the clippings somehow (e.g. have them taken away or thrown out) rather than just leaving them there. You can go to your town clerk's office and ask if there are any code(s) that may govern this; the clerk can either tell you or direct you to the correct department or person to ask. But if there is no local code or ordinance controlling what he can and cannot do with the clippings, he can put them anywhere on his own land that he wants.