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I had a similar situation. My dog was leashed, I was in my yard, and my dog got into it was a roaming pit bull. My dog definitely bit first.
I reached in to break it up and it didn't go so well for me. It did get broken up though.
I leashed the pitbull, walked around the neighborhood (bleeding) until someone recognized it and I dropped it off. Apparently the kids let the dog out.
I didn't report it for two reasons:
1) My dog started it. (even though he was leashed on my property)
2) I know what would happen to the pitbull, that seemed to be an otherwise well mannered dog in terms of people interaction.

The one I dealt with was quite different. He weighed 90-100 pounds. Built like a fire plug with no neck.
He attacked silently from behind. When I blocked him he whirled and rushed me without a sound.
His intent was to kill, not merely fight. (including me) My Yorkie weighs 6.5 pounds.
A neighbor said someone about a mile away has three PBs raised for fighting.

We have several "rowdy" dogs in the neighborhood. It's easy to settle them down.
This one was dangerous.

cb100rider wrote: According to the state of Texas, she's property and is valued as such, unfortunately. Texas is a crappy state to be a pet.

My reply was in the spirit of answering a moral question. But legal questions have answers too.

In a home attack, Texas does allow me to protect my property.

I made an animal attack report on the pit bull. I correctly stated the pit bull first attempted to attack my dog, but turned to attack me when I tried to prevent it. The policeman I discussed it with urged me to get a CHL for protection. Then he told me that if I ever had to fire my gun during a dog attack off my property to remember if the dog attacked ME it was self defense.

Luckily, in my case, there was no "fight" to reach into, or any injuries. When he started the attack on me, I snarled and rushed at him instead of backing up. I'm not sure exactly what he thought I was, but he stopped and backed off. He followed me for two blocks, but kept his distance. I guess I bluffed him good. Had I backed up or ran, it would have been different. Had I been armed, it would have been a justified shoot.

By the way, my dad taught me to never put my hands into a dog fight. A well placed kick is much safer and effective. I have done that, it works.

I voted that I would not shoot. But a clarification is in order.

My dog is not property, she's family.

Last month I backed down a charging pit bull while holding her in one arm.
So I already know I won't let anyone hurt her.