When someone talks bad about your dog

Since she is your neighbor and until you move, if you do, you have to put up with her so I think I would tactfully inquire as to what happened to her dashound and that you heard that she "thought" maybe your dog was responsible.  Did you leave your dog home in someones care while you were gone?  Maybe something happened that you haven't been told.  If not, then she is 10-96!

I agree, keep track of everything.
I think I would ignore her, dont let her draw you into her madness.
When she doesnt get a response from you chances are she will move on.
Good luck.

Man, this woman is a LOON! I, too, hope you can move soon.

It's my guess that anyone that woman talks to knows (or will soon) she's a fruitloop and won't take her seriously.  Try not to let the turkeys get you down.  If you're afraid she's going to report this to someone, take a dated pic of her dog.  You also may want to tell animal control that she's making false allegations, if they won't confront her. 

Angel--Completely ignore her, she's mentally ill and you aren't going to be able to rationalize with her or get anywhere with her.  Just keep yourselfs safe from her, watch out for anything she might try to do and keep looking for a new place. 
 
She needs help and she's probably not going to get it anytime soon.  It's going to take her husband or a family member to get that going and they don't sound like they are going to take charge of anything. 
 
AND--never put anything in writing that you don't want everyone to see.

Sara is always with me so there is no chance at all of my dog ever being away.
 
The person she told knows that she is not right. But I ma worried about her telling other people.
 
I am also worried that if something did happen to her dog that she would try and call the police on me. I don't know if I should let the police know what she is saying, or if I should just record the date and what she said to the OP and keep it in case something happens. She also told this woman that she took us to court and she won, and we now have to pay her for her loss. She is really taking this to the extreme.

Just pack up yourself, your family and your menagerie and move your butt up to Thunder Bay.  Houses are cheap up her and there's tons of space.  Plus I need another idogger around who gets me!  I promise Crusher won't hurt your duckies, he tried to nurse a dead baby bird back to life in the back yard.  I'll just keep the others away.  Stupid neighbors!

Everyone has replied with some really good ideas. I would keep track of all contact you have with her (or anyone at that residence). I would also, just for my own record, keep track of what people tell you that she says so that if need be you can pass that info along and the authorities can speak to that person about what was told to them. Naturally, hearsay isn't evidence so it isn't like you can call the cops and say "billy bob said that shirley joe said that betty sue said my dog killed her dog" but if something does happen that causes you to call the police then you can say "here is all my correspondence with psycho lady" and then if the police choose to go to billy bob and get the direct story from them that is there choice.
 
I would also, if you say the dog that sara supposedly killed, is barking outside in view now...take a picture so that if something happens later you have proof that the dog was alive. Its real easy for someone to show her a pic and say "is that the dog that was killed" and then when she says yes you know she is lying cuz the pic was taken 2 weeks earlier or whatever.
 
May not be helpful at all but at least it is documented for your peace of mind and may show any authority figure that you have being responsible and keeping track of stuff so your memory isn't altered.
 
Video would be great too.
 
Good luck, hope you can get out of there soon.