This is a commonly asked question because the problem occurs in nearly every residential neighborhood where aging landscape conditions exist. Code enforcement does not have the authority to require a property owner to trim or remove any of their vegetation unless it overhangs into a public right-of-way - impeding either pedestrian or vehicular traffic, or unless the vegetation is dead and presents a potential fire hazard.
Instead, this particular question is a good example of a civil matter between property owners. Code enforcement does recommend callers attempt to work this out amicably with their neighbor. (Any offending branches/vegetation may be trimmed back to the caller’s property line, as long as the trimming does not impact the future life of the plant.)