depends what you define as normal
.
In my experience girls don't do that often.
This girl most likely has some mental problems, like she feels that she should have a boyfriend, and is doing whatever it takes to get one for social proof. Be wary.
The bottom line is what do you want. Do you want a relationship with this chick? If you don't than you have to calmly explain to her that you're not looking for a relationship right now. Be as nice as possible about it.
hope this helps.