What are my rights re: neighbor/outdoor cat attacked my indoor cat who was sunning himself on my front walk?

I broke the fight up and chased Tito (neighbor's cat) off my property. Louie (my cat-age 8)) has lived indoors since we adopted him as a kitten and has never been allowed out to roam. He suns himself on the back deck or front porch/walk when permitted but comes right back inside. He is front declawed. He was diagnosed with a traumatic pneumothorax caused by punctures to his chest and nearly died Memorial Day weekend. Tito is known throughout the neighborhood as "mean" and routinely kills rabbits, chipmunks, squirrels and birds using just his jaws and back claws. He, too, has no front claws. The neighbors refuse to pay any part of the vet bills saying they don't know if it was or wasn't their cat. Bunk! We live on a cul de sac and have been chasing their cat off our porch and back deck for 5 years. I penny-pinched, refused over-night care x2, did IM antibiotic injections at home to save money after my cat's chest was tapped (surgical) for 175cc of air. Total -I visited the ER x1 and my vet office x2. My veterinarian ok'd my home care of Louie b/c I'm a peds nurse. We live in Ohio which has strict laws about dogs, but I can't find much about cats. I collected hair from the "scene" which includes my cat's gray hair and Tito's orange fur. Me and my 2 kids chased the cat away. These neighbors were our friends but they've been really rude inspite of our attempts to be calm and reasonable. What rights do we have? Small claims? The bills total $549.50.