As has been stated below, yes, you can make tenants liable for damage caused by pets. In fact, that would be true even if you did not have a written lease so stating.
However, it should be noted that the maximum security deposit you can require is an amount equal to 2 months of rent for an unfunished apartment. Any type of deposit counts toward this 2 month maximu whether you call is a last month's rent, security deposit or pet deposit. I recommend you simply take only a "security deposit."
It should also be noted that there has been an increase of demands by tenants to have a "comfort pet" as may be prescribed by a doctor. Under the Americans with Disabilities Act, you may be required to allow such pets.
Jeffery Woo, Esq.
Sedgwick, Detert, Moran & Arnold LLP
Complex Rental Property Group