Legislation recently introduced in Maine would, if enacted, make landlords "strictly liable" (legally responsible even if the landlord is not at fault) for injuries to any person caused by a tenant's pet.
Here's the language: "A tenant and that tenant's landlord are jointly and severally liable for damages caused to a third party by that tenant's pet. For purposes of this section, "pet" means any domesticated animal normally maintained in or near the household of its owner."