in the US, housing is not covered by ADA, it is covered by FHA (Fair Housing Act)
even though this is from Phillie, it is written based on federal FHA laws pertaining to Service Dogs
http://www.fhcsp.com/Publications/Service%20Animals.pdf
you might also find this helpful:
http://www.bazelon.org/LinkClick.aspx?fileticket=mHq8GV0FI4c%3D&tabid=245
Yes, you can be required to provide a prescription from your doctor --- essentially your doctor is saying you need a service dog or that you use a service dog
this has been tested in case law --- in one case, the landlord was allowed to require the disabled person to get approval from the doctor of his choosing (as an example of just how this can go if not handled properly from the beginning)
in the US, there is no federal requirement for certification & federal law allows for owner-training; however, anytime you claim your dog is a service dog, then you are subject to proving that the dog is, in fact, trained as a service dog
FHA laws allow the landlord to require you provide proof that your dog has been trained as a SD
-- there are also numerous case law examples on this one.. including owner-trained dogs
this is why it is highly advisable to keep a training journal & to also seek the help of a professional trainer (even if they do not train service dogs) so that you can have a professional trainer agree that the dog is trained & behaviorally suited for SD use based on their evaluation of having observed the SD-Team in action
in some states, you can be required to get licensing for your dog
those other "service dogs" might actually be "emotional support dogs" with proper proof from a medical professional... essentially, they are pets that are in the home to benefit a person who suffers from mental health issues
I have an owner-trained SD, have trained 5 other SD for other disabled people, and have served as "training support" for others who owner-train --- one of the things I always do is take dog through GCG as well as through Delta Society's Therapy Dog evaluation
some mobility dogs will have to be given allowance on CGC for a proper heal because their position when helping their owner walk is rarely, if ever, a standard heel.. .make sure the CGC evaluator is aware of the position your dog uses when working with you
some SDs are a little stand-offish on the TD tests... simply put the dogs are trained to focus on owner, not seek attention, and ignore attention given to them while working.... TDs need to seek attention & want attention... any good DS TD evaluator will work with you on this if they know your dog is being used as a SD & you are seeking TD evaluation as a measure of making sure your dog is "bomb-proof" and can handle complex, stressful situations.... they might not approve your dog for TD, but they can write what the dog excelled at, what the dog was not as good with (usually not as good in seeking & accepting attention) & how that behavior is desirable in a properly trained SD -- now, this does not mean your dog can react badly to any part of that test... it just means a properly trained SD might be a bit confused & frustrated with all the attention, but they should be able to tolerate it without any problems
what you need to do is (1) get that prescription from your doctor (2) document your training.... I mean try to recall time-frames... with details of what was trained.. include details about obedience training as well as details about the training that was specific to your disabilities (3) seek the support of at least one professional trainer & seriously consider getting CGC & TD eval
see this link & go to the place on the page that says "What should a letter from my doctor about my disability say to my landlord?" to get info on what your doctor needs to be writting down to help you support your use of SD
http://servicedogcentral.org/content/faq/61
EDIT TO ADD: many owner-trainers will seek a third party (professional dog trainer) to evaluate them based on ADI Public Access Standards ---- I have also done this with every dog I have trained & have recommended it for every dog I have been involved with
you can read more about it here: http://www.assistancedogsinternational.org/standards/public-access-test/