Answer. Here is a short summary of the law regarding “service animals” and “assistance animals.”
Service Animals. A “service animal” under the federal Americans with Disabilities Act (“ADA”) is limited solely to dogs that have been individually trained to work or perform tasks for a person with a disability, e.g. guiding people who are blind, alerting people who are deaf, or protecting a person who is having a seizure. The ADA does require that landlords make reasonable accommodations for residents with disabilities requesting to have a service animal. Note that the term “disability” under the ADA is very, very, broad.
Although service animals must be on leash or harness, they may also be controlled through voice commands or hand signals. Service animals are not “pets.” This means, among other things, that certain park rules for pets, such as requiring residents sign a Pet Agreement, cannot be required if it is a service animal. Dogs whose only purpose is to provide comfort or emotional support to a resident do not qualify under the ADA.
Assistance Animals. Under the Fair Housing Act, as amended, housing providers, including manufactured housing communities, must make also “reasonable accommodations” for persons with disabilities requesting to have an assistance animal for emotional support, or to provide other forms of help.
Similar to service animals, assistance animals are not regarded as “pets,” and residents cannot be required to sign a Pet Agreement for them. According to the Fair Housing Council of Oregon (here), as assistance animal:
“… is an animal that works, provides assistance, or performs tasks for the benefit of a person with a disability, or provides emotional support that alleviates one or more identified symptoms or effects of a person's disability. Assistance animals perform many disability-related functions, including but not limited to, guiding individuals who are blind or have low vision, alerting individuals who are deaf or hard of hearing to sounds, providing protection or rescue assistance, pulling a wheelchair, fetching items, alerting persons to impending seizures, or providing emotional support to persons with disabilities who have a disability-related need for such support. For purposes of reasonable accommodation requests (the law does not require) an assistance animal to be individually trained or certified. While dogs are the most common type of assistance animal, other animals can also be assistance animals.”
Companion Animals. A “companion animal” is more of a generic term, and the role it serves is what determines which laws will apply.
Approval Requirements. You are correct that you may not refuse to permit an assistance animal or service animal based upon size or breed. This means that you may not, based upon an animal’s “propensity” restrict a resident from having a particular animal. There must be some evidence of actual risk to persons or property, such as history of such conduct.
The one limitation where it appears there is some latitude, where the landlord’s liability insurance carrier would increase the premium or deny coverage. However, according to the Fair Housing Council of Oregon, even this issue could be problematic for landlords, unless they first sought, as a reasonable accommodation, to obtain another liability insurance carrier that did provide coverage. I suggest that if/when such issues arise in your community that you check first with your attorney to determine how to proceed. Better safe than sorry!
For a very good summary of reasonable accommodations under the federal law, go to: http://www.hud.gov/offices/fheo/library/huddojstatement.pdf
 An individual with a disability is defined by the ADA as a person who has a physical or mental impairment that substantially limits one or more major life activities, a person who has a history or record of such an impairment, or a person who is perceived by others as having such an impairment.