I’ve heard this stat before, but comparing to large cities.
NY is generally safer than Chicago, LA, Seattle, Boston, and Fort Worth; Wikipedia places it in 59th place for most violent crime per capita amongst the nation’s largest 100 cities.
The problem with any of these comparisons is that cities are very heterogeneous. In Boston, the Back Bay != Roxbury and in NYC, the West Village != the South Bronx. However, at least absent a doorman, I probably wouldn't leave a door unlocked or an accessible window ajar the way I routinely do in my (only) semi-rural home in New England. When I visit people in cities, I have to consciously remember that they'll be unhappy if I am casual about such things like I am at home.
NY is generally safer than Chicago, LA, Seattle, Boston, and Fort Worth; Wikipedia places it in 59th place for most violent crime per capita amongst the nation’s largest 100 cities.