first they will assess how likely they think it is that you will act on those thoughts. this is based on, what methods you are thinking of (if you don't have a method it is good, if it is something that a lower percentage of people die from like OD it is better than say a gun to the head) on your family history, they will probably ask you if any family members have killed themselves (some sources say that suicide is 40% inheritable) if you have attempted suicide before, and on your current state of mind.
even if they think you are diffidently going to do it, they still might not call the police, they might escort you to a mental hospital or to a normal hospital, or they might just call for the police to escort you to the mental hospital (you won't be arrested, you have done nothing wrong)
if they don't think you are likely to act on those thoughts in between when you tell them and the next time you see them, they might adjust your meds, advise that you admit yourself to a mental hospital, intensify your sessions, give you their home phone number and chrisis phone numbers.
my advice, if i can offer it to you, is that you should tell him/her. You will not get into legal trouble and depending on your age they shouldn't tell your family unless you are actually admitted to a mental hospital (in which case i don't know if they'll tell or not). Anything is better than ending your life, i'm sure your family would be happier to see you in a mental hospital than in the morgue. Don't hinder your chances at life because you're scared, you have so much to offer.
EDIT: from what you just described, i really doubt that your therapist would put you into a mental hospital. it's what your there for, to get help. telling him would be a good idea