Who is liable for injury and death of tenant's pet?

Our tenants are keeping 1 dog and 1 cat at the house which our PM has added in an Animal Clause term and condition to the original lease stating tenants are to indemnify landlord for any damage caused by these pets. we have a concern about who is liable to the tenants properties inside the house?
In particular who is liable for the life and health of their pets? For instance, what if the cat falls off the roof from a loose roof tile and breaks its legs? Can tenants give us a Breach Notice and try to claim for cat's medical bills and related costs?
Are the dogs and cats considered as tenants? or they considered as belongings of tenants?
We have landlord and building insurance, would that be enough to cover?
Many thanks.
Good question.

I currently have a vacant unit being advertised for rent and have just sent an email to the PM asking that she edit the ad and say "small pets considered".
I looked at my competition in the area and all of them say "strictly no pets" so i thought i was being clever and filling a niche which will increase my chances of renting the property sooner.

I've told her i'll consider applicants who have a pet cat but if they apply to rent then the standard/relevant clauses should be included in the lease:
1) carpets are professionally cleaned when vacating with receipts provided as proof.
2) property is professionally sprayed for fleas when vacating with receipts provided as proof.

Maybe i should ask her to also include an Animal Clause term and condition like you have. What does it say?

Hopefully it's worded correctly and covers all your concerns, i.e. the tenants assume full liability for any damage caused by their pet to the property and/or any visitors to the property and the tenant also takes full responsibility for the health and life of their own pets.
Thanks shuggy, they are real good reference. Looks like we will have to discuss it with our PM to add in more extra clauses!