Should I Pay the Vet Bill?

What is the name of your state? Ohio

One evening as I walked out of my house, my dog darted out, ran across the street, and attacked a dog who was being walked on a leash.
The dogs were separated fairly quickly and I apologized. The lady said "Don't worry, I think my dog is okay, he's just scared"

Almost a month later, I received a letter in the mail asking me to pay the veterinarian bill for his check-up because she found blood on her dog's chest later that evening.

I would like to pay the bill and send a letter of apology and be done with the matter.
If I send the money and the letter, is this case closed, or am I opening myself up for a lawsuit if I admit wrongdoing?

Thanks in advance for any advice,
Lisa

State what you want.

If you are agreeable to paying the vet's bills for this one, isolated incident, simply draw up an agreement stating so. Have both partys sign to the agreement, and date it. Specify that you are paying only for the vets bill from this one incident. You are the guilty party for being negligent. The faster you resolve this issue the better your chances are for not being sued at a later date because "Fido" has suddenly developed heartworms because of your dog's attack.
In My Humble Opinion.

Also, under no circumstances should you write a letter of apology. It's a shame, but in this day and age, you're just opening yourself up to a lawsuit. I do think you should pay the vet bill, if you think it is legitimately related to your dog's actions.