Personally, I'm very paranoid when it comes to this. Most of my therapists knew or know I'm suicidal and have been for many years but they do not know to what extent (constantly thinking about it on a daily basis, already having everything I need to go through with it). I'm wary of telling them everything because I was already sent to hospitals because people thought I was at a high risk (which, I guess, is true and has been for quite a while but it's not like locking me away would ever help with that).
So I'm careful when it comes to telling them. In my experience many are quick to put you away once they find out that you have a plan, the means to do it and constant suicidal ideation.