You can do it in a public hospital, but about the only way is with a psych referral. It's not hard, you can get a free referral to a psych from your GP and they can help from there.
Basically you just have to prove that it would cause you mental anguish. It's not that hard. I wish I had done it with my first as believe me, a lot of the heartache and stress that initially stopped me from bonding with him would have been avoided.
Just be aware that some of them will try to browbeat you. Some will try to push and say that it's what's best. You have to do what's best for YOU. I had a terrible, TERRIBLE labor with my DS and I don't care what anyone says, I won't experience that again if there's a way to avoid it.
Be afraid. Every mum is for her first. But be in control as well. And don't forget that a natural birth can be (and will be) extremely difficult, but the result is something you won't give up for the world.
That being said... Trust your instincts. Trust in yourself and your choices.