I guess there are differences in national/regional responses to such disclosure. In the UK and from personal experiences, admitting and struggling with suicidal ideation is dealt with only if you plummet feet first down that path... which I personally think is pretty irresponsible and dangerous... but budgets are budgets.

I would advise that if you’ve experienced overkill responses to admissions, then balance up the pro’s and con’s of if you do vs you don’t.

If you think you are at risk, then it is going to be reassuring that you’ll be taken seriously and given care rather than shrugged off.