It depends where you live, your hospital and their policy.
From my experience, a suicide attempt doesn't necessarily mean an inpatient admission. It's your mental health at the time which determines that, if you have 'insight,' and if you have no support outside of hospital and they think you're that unsafe.
Being an inpatient can help or make people worse depending on what care they provide- and your personality...personally, it makes me worse. I think it does that a lot to people who go into my local psych ward, only they can cope with it much better than myself.
Do you know anything about your local psych ward and what they do?
Do you have a therapist, or any support? Have you been an outpatient? That can also be an option if you present yourself at A+E, and your hospital provides crisis intervention.