Service animals are not pets. However, you should still notify the landlord from the start that you have a service animal.
Bear in mind that regulations in housing are not the same as they are for public access. Though a business cannot ask you for proof of disability or proof of training for the service animal, a landlord may. This is because the duration of the relationship between landlord and tenant is much greater than that between merchant and customer.
In a situation where the landlord has a "no pets" policy in place, you are required to submit a letter requesting a reasonable accommodation making an exception to the "no pets" rule to permit you to keep a service animal.
Access in housing is different than public access. While they could not ask for proof of training in a grocery store, they may be able to in a landlord/tenant situation. This is because the duration of the relationship between landlord and tenant is much longer than that between merchant and customer.
Here is a sample letter requesting a modification in pet policies to permit a person with a disability to have a trained service dog reside with them: http://servicedogcentral.org/content/node/285
If the dog is an emotional support animal, rather than a service animal, use this sample letter instead: http://servicedogcentral.org/content/node/215