Taming a kitty

There is a beautiful white-and-tabbie that sometimes looks in my apartment from the outside window. I think it is a stray and I would like to tame her and have her fixed so that my sister can adopt her. The kitty, I call her Little Pie, will look at me with very wide and friendly eyes if I talk to her through the window but I'm not sure if she can actually hear me or if she's thinking 'What's wrong with that crazy human?' However, if I go outside, she instantly runs.

The last two times I've tried to talk to her, she ran down the hill and rolled around at the bottom the whole time I was talking to her like she wanted to be friendly but since she had ran when she saw me coming, I was afraid to go down and try to pet her. When she was bored with rolling around, she walked away into the woods behind my apartments, though she did turn and look at me for a while before disappearing.

I've tried leaving food out for Little Pie, wet and dry, but she must have other places she goes too because she sometimes she'll return and eat and sometimes she won't.

If someone could give me a few pointers on how to let her know I want to be her friend, please let me know. My sister is already planning on giving her a safe and happy home if Little Pie can be tamed and adopted. We want her to be happy and we want to know she is safe.

Well,

I don't know what the others might suggest, but, since she shows signs of friendliness, and rolling. And if you can take her in your home, a 'live trap' with food in it may be in order. You could trap her, then put her in a safe room, bathroom or bedroom. After the initial trauma, she will adjust quite quickly, considering you will be her only food source. If she isn't feral, she will know that she is safe, and learn how to accept the love.

If others, with experience, happen to disagree, I defer to their expertise.
I'm just using common sense, and I do foster a lot of cats and kittens that have been trapped or abandoned.

If you do take her in, please have her tested for FeLV/FIV BEFORE she enters the house. (take her to the vet in the trap, the test is quick)
Also, since she's out in the woods, I'd go ahead with the Rabies vaccine, if she is Neg/neg for the other two things.

This cat sounds like it is what I call "scarel", not feral.. She just needs some time and one-on-one contact. I have socialized too many cats to even number, so I have alot of experience with these type. I agree that humanely trapping her is best. Get her spayed and combo tested and vaccinated. Then bring her home and put her in a small room or bathroom. Feed her well and attempt to play with her once daily with a feather toy or lazer light to get her attention. If she is young especially, then she will respond to the attention very well. Don't force her to go too fast, and if she lets you know she wants to be left alone, then show her the respect she is asking for and leave her alone.. She sounds like she is timid but not really afraid. Taming her may take a day or a month, or in some cases even longer.. But she will be worth it! If you need more advice on socializing her, please feel free to email me privately or check out my website at www.shadowcats.net for more info. Also check out this link for taming advice: http://www.alleycat.org/pdf/taming.pdf.

Good luck!

I know this is going to sound crazy, but this is how I have gotten several stray kittens that were very wild to come to me...
I sit very still and meow to them in a high pitched kitten meow. For some reason they must think or remember this type of meow from their sibblings I'm assuming, and it has worked every time. It might take a little time sitting and meowing to them...and dont worry what your neighbors are going to think of you, mine have come to understand what I'm doing, they just call me the crazy cat lady now, LOL! But seriously though, give it a try and see if that works.