If you accept pets then I'd suggest looking up a simple "pet policy" on google and using that as a template. 

Missed seeing the toucans and parrots above the house.

We changed two things - no more fire pit - due to new HOA rules and no pets.  

What responsibilities are the tenants (Utilities, fees, pets, etc?) 

We have strategies to mitigate that risk: not renting to locals, smaller units, multiple-day stay requirements, no pets, must have a picture and at least one other review on your platform profile, must respond to an email from us, exterior cameras, etc.And 99% of people naturally tidy up after themselves.  

Another tenant in the same building asked us if we would allow a cat (we had no pet policy).

Also I can require a non refunable pet deposit of 200 or increase the rent another 25$.

I know most landlords hate pets in their rentals but, as a spoiled-dog owner, I can attest that there are some people out there whose pets are MUCH less likely to ruin your place than any child under 8 years of age, lol.

Think of what must happen inside a house for people to absolutely walk away from it and not even try to sell it.You WILL eventually run into the following:A house that has had too many animals, either pets or infestation.Mold / Grow operationSquatters/ human waste/ house stripped of all copper plumbing and wireCaveats/ liens against the property that have to be paid prior to change of title.Do as must due diligence as possible prior to the auction, hope for the best, expect the worst, and have a good remediation team on hand. 

Could I have a no-pet policy in this situation?