Is she a nut case?

Yes, but your zombie statement indicates that you two are a perfect match.

Don't get insulted, but is your job devoted to spreading ignorance?

Could you explain (or re-write) your comment:

I am sorry for my mistake, here is with the correction.

She also said in the letter that she don't know me but trying to know me well, I am not sure what to do with her because on one side she says that she is trying to know me but on the other side she says she don't trust me to share her number with me? She is really very shy and reserve person and it is difficult for her to get along with new person. I am thinking that if she can't trust me on phone number how she would trust me at all or than how long it will take her to trust me.
I hope you understand now. Any suggestions would be highly appreciated.

Don't get insulted, but when you make zombie statements, it doesn't look so good.

Okay, you want a serious answer? She is weird and unfocused. A nut case? Hard to say. But do you really want someone that wishy washy in your life, who can't even make up their mind as to whether they like you? This is a tease at best.

I do not think it is a "tease" as does Jespah...but I think the girl is, as you indicate, shy and not sure of herself.

She is not sure of how to express the things she is trying to express...and what happens in those cases is that a person just keeps digging a hole deeper and deeper.

Get to know her a bit...get her to relax with you...and this will almost certainly clear up. She may appreciate you understanding her personality problems...and things could get real good between you.

Don't over analyze in interpersonal relationships, because you are almost asking for trouble.

Just be cool.

If it progresses, fine. If it dies...there are more fish in the sea.

Really a deep insight and I really appreciate every single word you said, Thank you so much. I completely agree with you that she has some personality issues and in some way she tried to indicate those things. I don't want to bother you with this but I must tell you that I am very outgoing person even though if I have a worst day or some extreme problem somehow I have this skill to act fresh, normal and happy in front of the people. May be it is because I'm an stage actor or may be because I don't want to show everyone how miserable my life or some particular situation is. But there are some very few people who are really close to me and I can be myself when around them and can discuss everything with them. My intention was and still is to know this girl before I disclose my deep inner side but also I never tried to be a charming, handsome, happy kind of a guy around her. I was just how I am but I think she took me wrong I don't understand why? However as you said I will give it a shot, I will answer her with a letter and than see what she has to offer. Once again Thank you very much for your time and your genious thoughts. Take care

Thank you for your comment and I don't feel insulted. By ''zombie'' thing I meant was that how come people in this world can be so strict about calling someone from there phone despite after meeting them 3 times. I mean what is the big deal, what harm one can get if there number shows on someone else's phone? For me this is a big sign of insecurity because one thing I'm sure about is that no one can call you or force you to answer the phone unless you want to do so at least in this country I'm living.
But instead writing someone a letter and telling him Oh.... I want to know you but I don't want to call you because I don't trust you.... Seriously!
But dear when I said the Zombie thing I meant in a funny way, you see I have a bad humor. Any how may be its just me who thinks like that . Thanks again for your time and your thoughts. Have a fun week end.