She is scared, and this is very normal behavior.
First of all - because she was so friendly outside, are you sure she wasn't a neighbor's pet? Most cats, when they escape outside, remain within a three-block radius of their homes. Perhaps take a pic of this kitty and hand it out to your neighbors to make sure someone's not missing a pet?
Also, even cats that were pets will revert to feral behavior to protect themselves. It sounds like if this kitty doesn't belong to one of your neighbors, that she is a stray that at one time did belong to someone. Ferals are never that friendly that quickly!
Also - I didn't see you mention whether or not she's been spayed? If not, she really ought to be. If you want more information about why, please click on the link in my signature line and/or here's a great article in the "Care" section of TCS: Spay and Neuter: The Best Thing You Can Do for Cats!
But now that she's inside, she's scared. Cats are very territory oriented. Dogs are people oriented, and wherever their people are is "home." Cats, on the other hand, are very comfortable in their territory, and very uncomfortable out of it. They like regular schedules and no disruptions to their routine. All of our kitties are ferals, and several of them regularly roam "patrol" to make sure everything's in its place. When we move something, even it's a chair that was on the other side of the room, it gets very close inspection, LOL!
Socializing a feral, which is how you would have to treat this situation, can be fairly easily done, especially with a kitty that was friendly - but it takes time, and the ONLY way to do it is on the cat's schedule.
Even when you bring home a hand-raised kitty, you should expect them to be scared, and the same rules apply for brining a new cat into any home, really.
If your sister wants a "ready-made" loving cat, this kitty is not for her. However, any cat or kitten really needs the same method of introduction to a new space. Cats require patience and work to earn their trust, get them used to the new territory, etc. Especially so for ferals or strays.
Kitty should be confined to one room. Any more is overwhelming. No other animals should have access to this room. Put litterbox on one side, and food and water on the other. Make sure there are a few toys for her to play with when you're not there. Kitty has to get used to this room before being allowed into a larger area, and kitty has to get used to its new person. This is best done by NOT INTERACTING with the cat at all. Sit in the room, read to her, sew, do your homework, whatever you have to do. Leave a radio on - with a classical station playing. This is calming. Leave a night lite on. Dark but not black is also calming for them. Get a sweatshirt or tee-shirt all sweaty, and place this under her food bowl. The idea is not to get kitty used to your smell, the idea is for kitty to associate your smell with good things.
The bottom line - get kitty used to you and the space. Don't look at kitty - wait for her to come to you. They'll let you know when they're ready to play, or for pets. Even though this cat was friendly outside - which is a very good indicator she'll be friendly and loving inside - she still needs time to adjust to the new space, whether it's your basement, your sister's home, or someone completely different that will be adopting this cat. But when she's adopted out, not only will she need to get used to a new territory, she'll need to get used to the new person.
There is a product you can buy that will help her transition. It is called "Feliway". It comes either as a spray or a "plug-in" (like scented oils). It is a synthetic pheremone that mimics the scent in the scent glands in cats cheeks - which is a "friendly," not a "territory" marker. This has helped in our mulitcat household, and it can help a cat feel comfortable in a new territory.
Here are some links to threads and articles with very useful information:Bringing Home a New Cat
...and although this is the story of socializing a true feral, the same principles hold true:Socializing a Feral: the Story of Lucky
Thank you for rescuing this kitty!!!!!!!!!