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

The OP is asking about criminal sanctions, but it seems to me the bulk of the responses are discussing whether there is any civil liability for a failure to rescue.

I think there are only a very few states currently imposing a criminal penalty for failing to report or rescue the victim of an emergency. More states criminalize the failure to report instances of specific victims of specific crimes – that is, anyone who is aware of a minor who is the victim of sexual assault, for instance, must report it or face criminal penalties.

We discussed this issue several years ago: