What crime would someone be charged with if they chose not to save someone's life?

IIRC, the Kitty Genovese thing was, MOL, an urban legend.
I’m too lazy to look up the facts, but, what happened was too long and confusing a tableau for any of the locals to be able to pinpoint an action that could help, there were some calls to the PD, and the newspapers were basically omitting a bunch of facts. Something like that.