In the city, you could run into a problem with a neighbor who takes over your sidewalk garden. Sidewalk gardens are small spaces intended to be designed and cared for by the residents whose property adjoins them. They may have a tree and a small patch of ground where the resident can plant.
Also known as a pit garden, the small area is designed to beautify the city. Since residents are intended to make each pit garden their own, they shouldn't be asked to remove their plants or decorations unless the city itself requests it.
The pit gardens are overseen by the Parks Department and aren't individually owned by residents, but that doesn't mean certain residents don't have rights to them. No one has the right to ask anyone to remove their decorations for pit gardens outside their homes. The Parks Department actually encourages individual development of the plots and doesn't require them to look the same. The Parks Department encourages people to develop the plots outside their homes but doesn't look kindly on others from out-of-the-area changing plots that other people in their own residencies have already developed.
In cases like this, you may need to reach out to your local Citizen Committee, since this organization helps mediate issues. If someone rips up your space or damages your property, then it's within your right to pursue a direct claim against the individual responsible. No one should touch your personal property or the items you've placed in a garden without permission; they only have a right to change pit gardens near their properties.
Source: The New York Times, "Disputes Over Sidewalk Gardens," accessed Dec. 14, 2017