The answer to this question is usually no, your emotional support animal is not a service animal. Service animals are defined in the Americans With Disabilities Act as “any dog that is individually trained to do work or perform tasks for the benefit of an individual with a disability, including a physical, sensory, psychiatric, intellectual, or other mental disability.”
Emotional support animals are typically not trained to “do work or perform tasks.” By their very nature and relationship with a particular human, they are comforting and understanding, but they weren’t trained to be that way and they don’t need to apply any skill or effort, as if it were work, to be that way.
Service animals, which are specifically dogs and occasionally miniature horses, are permitted on public transportation and in public facilities when they are on duty and under their handler’s control. Emotional support animals, because they do not perform tasks on behalf of their handler, such as opening doors or navigating to a location, are not required to be allowed into public facilities.
Your home, of course, is not a public facility, although there may be grounds and common areas outside of your unit that you share with other residents. The Fair Housing Act does require housing providers to permit emotional support animals in individual residents’ units when those residents have a disability, can prove that the animal satisfies a disability-related need, and request permission for the animal to live there as an accommodation for the disability. Read the linked document to find out about other factors that are considered that can outweigh a request to have an emotional support animal in a housing unit.
Sometimes, state laws provide additional access and protection for service animals and emotional support animals. Here is a chart where you can find your state’s laws about assistance animals.