I am hoping to find clear definition as a residential property owner, would/could I be held liable if a tenant's dog bits and injures someone? If the victim is looking for retribution, could I be held responsible? I'm thinking laws may be state specific? Any advice is much appreciated.
You'll want to read this article:
Without exception, you will want to require your tenants to carry Renter's Insurance and have a strong pet addendum - including a photo of the pet, breed (non-aggressive only), the pet's medical records to show all vaccinations are current, more...
And, if a dog bites anyone (other than someone breaking in or the like), you will need to act to have the pet removed from the premises to ensure you do not assume liability.
You can bet that you will be sued. As to whether or not you will be Liable for the damages, that will depend on what happened.
Patricia's advise on requiring tenants insurance is good advise.
You need to check with your insurance agent. There may be breeds of dogs that will cause your carrier to cancel or non-renew your policy. You need to know if that happens, do they have other companies that will write you with that breed of dog.