If the dog is certified, he should be covered under fair housing and american disabilities act. I would still be forth coming with the rental company.
Depending on the state laws, they are still usually able to require that you pay for any/all damages including if they feel there is pet odor in the carpet.
Good luck and double check the local laws on ADA. Whoever you got the certification with the dog should be able to helpo you with this.
If he is Not certified, they may not have to recognize him.