New York allows the use of force for self defense when the person has a reasonable belief that they are in immediate danger. Deadly force maybe used when the person believe that; the aggressor is about to kill them. Also when it's to prevent a rape, robbery, kidnapping, or burglary.
Castle Laws are laws that address the use of force when defending one's self inside their home, or on their property. Some states expand this to vehicles, and the person's place of work. Castle Laws generally include: the places where this law applies, the requirements fro use of deadly force, if there is a duty to retreat, the amount of force that maybe used in defending one's self or others. These vary widely from state to state.