how to escape relationship

Please help me!!! I've been involved in a relationship that has put me into misery for a year and I really want to call it off, but I see no way out.

It started a year a ago, I met her in another country while travelling and she is kind and gentle and everything. Eventually she traveled to my country and stayed with me, thats when problems started. Her emotions are like a roller coaster, or rather someone with bipolar disorder, sometimes her feelings are hot and intimate but other times she goes crazy, has no confidence in me and wants to leave. I've lost count the number of times I had to beg to make her stay because I really wanted to stay with her.

After a year of doing that on a weekly basis, I've finally ran out of steam and completely lost confidence in the relationship myself. I'm getting headaches and I'm in misery. Because of that I'm sad all the time and every time when she sees I'm sad she's calmly ask if I want her to leave, doesn't matter what I say she'll start going all emotional and cry, starts saying "I'll leave next month"....then suddenly "I'll leave right now", then starts packing and eventually it always comes down to "I'll go commit suicide".

My conscience wouldn't allow me to let her die, so I end up begging to make up. This has happened so many times and now I've even lost the will to beg, so a couple of times when she says "I'll go commit suicide" I let her leave. Then she'll come back after 15 min and tells me she took a couple of sleeping pills. She just sits and cries and gets all drowsy. So I spends hours watching her and get ready to call the ambulance if she loses consciousness, but she always end up fine.

I don't want to involve the police or ambulance cos I feel its just attention seeking behaviour and I'll be wasting their time since it's not an actual overdose. So now I'm stuck, trying to put on a happy face. She refuses to move out or go anywhere, no amount of reasoning will change her mind, refuses to see a psychiatrist, and I just live in fear of her emotions. Jesus, I'm not joking about this, if anyone has any ideas about how I can escape without her pulling another stunt, I'm all ears.

Unfortunately we're living in an apartment that is rented under my name, so I can't just disappear even though I've thought about it.