Report the threats to the police without pressing charges. ... .Cover your ass, man.
Just FYI, in many jurisdictions at least in the US, it's not up to the victim whether to "press charges;" prosecutors make the decision and often proceed even when the alleged victim doesn't wish to. Not saying that to discourage you from reporting the threats, but to ensure you don't have an ill-founded sense of control over what happens then.
As to "I don't feel anything," do you mean you feel numb and non-reactive when you hear her say these things? You may be able to identify them as the product of mental illness and thus not react to them, in the way that you might not particularly react if someone close to you was suffering from schizophrenia and said obviously delusional things.
It isn't pleasant, but if you know for sure not to take the comments seriously or personally, you may just be doing a mental version of hitting delete.