Typically, a person is not liable for veterinary bills under the circumstances that you describe. Their can be exceptions. If this person brings a claim against you, you can turn it over to your homeowners insurance. You may want to contact an attorney in your area for further guidance.
This is not to be construed as legal advice. I do not have an attorney client relationship with you.
Sign up to receive a 3-part series of useful information and advice about personal injury law.