Frank, let me first say, I am not a lawyer and cannot provide legal advice. There are so many considerations and this person also has 2 additional pets to consider. If you do not allow cats and they have 2 cats that sounds like good viable grounds to deny.
As one landlord to another, I recommend you have a written pet policy/standard that you follow consistently with each applicant or you open the door for discrimination complaints. If you allow small dogs, then let your criteria be known to help people self-qualify.
Remember service animals are NOT considered pets but an “accommodation” so even if you had a “NO PET” policy service animals are exempt. The fines for denying a person a medical accommodation are quite hefty.
I strongly encourage you however to have written criteria because if you had that and this applicant was provided them, he/she would see that having those two cats would make them not meet your criteria and the two service dogs are a non-issue. Not having that criteria, and if you had any prior discussion about whether you allow service dogs or not, could make this applicant speculate or assume you are denying them for their service dogs. You want to avoid these types of issues in the future and having that written criteria helps you do that. It is in writing and self-explanatory and helps people know what your qualifiers are and whether it’s worth it for them to apply or not.
When creating your criteria I urge you to attend free local Fair Housing training in your area, and join your local Apartment Association to help you put that important document together. Best of luck to you. Teresa (Teresa@IETenantMatch.com)