Honestly, don't create more drama than necessary. Just stop talking with her and leave it at that. The only reason to talk to someone about your decision to go NC is if it's (a) part of boundary you are setting as a last ditch effort to repair the relationship, or (b) they are harassing you and you need to inform them it needs to stop.
But what I would do first is think through the repercussions of this decision for your dh and any dc, if you have them. Dh and I are NC with my entire family and we are also NC with one of dh's family members. Obviously, if it's your entire family, it just means you don't see them anymore and what's done is done, so a bit simpler. If it's just you who doesn't want to see SIL anymore, how will you handle Christmases and special birthdays for your PILs? What about your dc? What sort of relationship do you agree for them to have? What about for funerals or weddings? Will you attend and just not speak to her? Will you not attend? Will you not allow dc to attend? Think through long term what your boundaries will be and how you'll handle them before you take your next steps.
In our case, where we are NC with one family member, but not dh's entire family, this is due to safety reasons related to our children (this person isn't safe to be around our or anyone's children). We do not interact with him at all. Our dc aren't allowed to visit anywhere he is present including the house he lives in, even if he's not actually there. This means no family Christmases, unless we host. No birthdays. No weddings or funerals (dh would attend family funerals alone, and I would stay with dc). Family have been supportive and sometimes don't invite him so that we can attend, but it's not every single time, so we do miss out. It's a small price to pay for knowing my dc are safe and well though.
And then once you set your boundaries and know how you two will handle these various situations, then just don't speak to her. Don't attend events where she is present, if that's what you've decided. If she contacts you loads and is harassing you, send a short message to request that she does not contact you again. You don't need a big melodramatic song and dance about it. Just cut her out of your life if you don't want her there.