Do I have a Dog Bite Case?

I had a neighbors dog bite my dog who went into emergency surgery for an infection causing him to need a draining tube. We both had our leashes down in our complex but they were still on both dogs. They said they would pay half but then after animal law enforcement came, they told us we were being unreasonable (Even thought we told them its the law and we were going to call the weekend before a their apartment when speaking about the situation and how to fix it) and wouldn’t pay the half of the medical bill ($550). They dodged animal law enforcement that I had to give them her phone number and I have no idea other than the officer letting me know they were in contact and gave them the necessary paperwork. Do we have a case?