Found a dog on the street and don't know what to do

On my way home I found a yorkie dog running into the street… It was in a horrible area of town (ghetto) and traffic was bad so it was either I pick her up or she get run over. So I brought her home and she is very friendly but she acts scared around my dad almost like she has been abused. I'm not sure that's the case I'm just saying. She has really bad fleas but she is very sweet and loving. I called the shelter and I went on craigslist but didn't see any ads until I looked and saw one posted about a month and a half ago that matched the description. They said in the ad she got out of the fence a month and a half ago but when I picked her up there's no way she could have survived that long on her own. That area is known for wild out bulls tearing up small animals anyways and is really dangerous. I almost am thinking maybe she got lost again? They didn't put any contact info so I emailed the craigslist account and asked if they found they replied "no" and I said that I might have one that fit the description and they haven't replied! It's been days and they are writing off an iPhone so I know they read it. I don't know what to do. My family is getting attached to the dog and The last thing we need is a dog but I mean we will take it in I don't want her going back to a home that's bad and if they don't care. I'm trying to give them the benefit of doubt but they won't even reply to my message. I'm not a bad person I just want to do what's right. Any advice would be appreciated thanks.

Added (1). I'm pretty sure it's their dog it matches the description and location

So sweet of umyou but it looks like they dnt want the dog and maybe they are just think about it maybe;just like try meeting with them and ask them they want the dog or not if its impossible;well thats what i got.

Are you sure it's the right person? It might be some breeder who wants to breed for money, or it might be a mad scientist,

If everything fits her/his description of the dog its theirs if it doesn't than it isn't theirs.
Also, if that's the case keep her.

First thing you need to do is to take to any vet clinic or shelter and have them scan for a microchip. There may be somebody frantically searching for her at this point and no one knows you have her. If there's no chip then the kindness thing you can do is to take to the shelter and let them know that you found her. She can then get the medical treatment she needs and held for an owner to claim. You could always request that the shelter contact you for adoption if and when she goes up for adoption.

Give her the best chance possible. If the later occurs she will have vaccines, medical care and spayed if not already when you adopt her. And - who knows. An owner may show up.

Fist off if the dog has fleas, give him/her a flea bath. Period. You can use a flea/tick shampoo or Dawn dish soap.
Secondly, make sure he/she has no mats and is brushed out well. Then apply a topical flea medication (Can be found at walmart) although a pill called Comfortis or a thing called Revolution is ideal but can only be obtained by a vet. (Maybe 1-800 PetMeds) but I doubt it.

I would make sure she has a good food to eat (Blue Buffalo, Natures Variety, Purina Pro-Plan) this can help with getting her healthy again. If these people don't message you back then either
A.) Keep the dog
B.) Find a rescue (yorkie rescues are very easy to find)
C.) Re-Home them

DO NOT TAKE HER/HIM TO SHELTER IT WILL TRAUMATIZE THEM!

If they don't reply, I would contact the police and just say exactly what has happened then they will decide to take it of your hands or not

Thinking about this logically, even if they replied to all your messages it would not be a very good idea to give the dog back to them. A good dog owner will reply As soon as possible but the kind of communication you have right now shows you how concerned they really are for the animal. Honestly in my opinion I think you should either keep the animal, give it up for adoption, or hand it over to a trusted dog adoption agency. There's no real proof that the content of the craigslist listing is true so beware. If they were previously abusing their dog and it ran away due to fear, the owners could have easily written that it had escaped from their fence. What you decide to do is really up to you but make sure in the end the poor pup ends up in good hands.

Maybe you can go to a vet and ask if they can check if the dog has a microship, if he does, the owner can be contacted

They don't deserve the dog back. Most people are overjoyed to find their missing pet. Keep the dog or find a rescue as that lil' dog would thrive in a loving home.