My neighbor walks around her backyard topless and I find it very offensive. Is it legal for her to do this

Indecent exposure usually requires an intent to offend. If she's in her own backyard and you've got your nose over the fence I agree she's doing nothing wrong. On the other hand if she's flaunting it she may be in the wrong depending on the way your state law is written.

I agree with the first answer, however, in many states there are now laws that say a woman is allowed to go topless because men can go topless and the Courts have interpreted the law to be prejudicial if women can't do the same. Moreover, it appears that she's doing it in her own backyard. Instead of being outraged, why not simply ask her nicely if she'll refrain from doing it any further or erect a fence high enough that you'll no longer be bothered by her display.

Good luck.

You called the police, they told you it is not indecent exposure. The only other remdy would be a civil lawsuit but the outcome would be far from assured.