This is a Fair Housing Act issue. In housing, a disabled person has a right to keep a pet for therapeutic/companion purposes as an accommodation. The dog does not have to be a "service dog" as that term is used in the context of the ADA. The first step a renter must take is to make a written request for the accommodation. If there is a doctor's note, then there is really no basis for the apartment manager to deny the accommodation. But if they do, then you can file a complaint with the local housing authority, or with the state or federal housing authority, or you can retain an attorney to challenge the denial of the accommodation. But the first step is to make the request in writing and be clear that you are asking for an "accommodation" pursuant to your rights as a disabled individual under the Fair Housing Act.
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Under the ADA an "emotional support animal" is NOT a service animal, meaning that a landlord can refuse to rent to a person that requires an emotional support animal if the property does not allow pets. I could not find any Kansas law on point, so the state likely follows the ADA.
The Johnson County Department of Human Services may be able to give you a more definitive answer: http://hsa.jocogov.org/
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