i recently adopted a stray under similar circumstances. she was clean, seemed healthy, and was extremely friendly, so we couldn't imagine initially that she was really a stray. well, she was actually half starved to death, her pads were scraped and torn, she had fleas, worms and ear mites, and at 3 pounds she was carrying a litter of 6 kittens in her(as we learned when she was spayed). we brought her in and fed her, checked the lost&found boards in kijiji.com, local supermarkets, phone poles, etc. no one was looking for her. don't let friendliness fool you, some cats just have amazing personalities even in the worst conditions.

Britomart has now probably put on 2 pounds in the month we've had her, she's free of mites/fleas/parasites/kittens, and she's turned out to be the absolute best cat we could have hoped for. cats in need have a knack for finding sympathetic people, and even a healthy seeming stray can be surprisingly close to meeting their end.

if that cat isn't a stray, the worst that happens is you return it to its owners when they post that she's missing, but you could end up with a happy, grateful pet.