Under the law, you can’t prevent a tenant from bringing a pet into your property, unless it is a condominium and the building declaration says no pets. So even if a landlord and tenant sign a lease that says no pets, the tenant can bring 2 dogs and 4 cats the next day and there is nothing the landlord can do about it.
Yet if the landlord has a no pet policy in the entire building, they can probably refuse to approve the tenant in the first place if they know the tenant has a pet. You start to see the problem. If the tenant is honest up front and tells the landlord they have a pet, their application can be refused. If the tenant lies on the application and then brings in a pet afterwards, there is nothing the landlord can do. The result is often a poisoned relationship, right from the start.
As a landlord, you can include a “no pets” clause in the lease, but this clause is automatically void, so there is nothing to stop a tenant from getting a pet (or pets) even if this clause has been added. Pets can cause a lot of damage, and it can be difficult for a landlord to recover the costs of fixing this damage from the tenant, as it is illegal for the landlord to ask for a security deposit. So a landlord can decide not to approve an honest tenant who admits he has a pet, but can do nothing once he has approved a dishonest tenant says he has no pets but really has two big dogs. Pretty stupid law if you ask me.