Pet deposits on emotional support animals?

I moved into an apartment 10 months ago with my two dogs and was required to pay an additional $1000 upon move in as a pet deposit. Since the time of move in, my psychiatrist issued me a written note on a prescription pad stating that I required my dogs as emotional support animals for a medical condition that I... show more I moved into an apartment 10 months ago with my two dogs and was required to pay an additional $1000 upon move in as a pet deposit. Since the time of move in, my psychiatrist issued me a written note on a prescription pad stating that I required my dogs as emotional support animals for a medical condition that I have. If I move into a new apartment, they won't charge me a deposit for my pets because they have been prescribed to me. I would like to ask for my pet deposit to be refunded to me for the apartment that I am living in currently. Is the management company required to refund my deposit since my dogs are now prescribed to me?
Update: Thanks for the feedback. Just to clarify a couple things that came up in responses: 1.) The other place I was looking at would waive both the pet deposit and their "no dogs allowed" clause. This seems to be pretty standard. 2.) The pet deposit that was paid for my current residence is completely refundable... show more Thanks for the feedback. Just to clarify a couple things that came up in responses:

1.) The other place I was looking at would waive both the pet deposit and their "no dogs allowed" clause. This seems to be pretty standard.

2.) The pet deposit that was paid for my current residence is completely refundable barring any damage.

It is my understanding that as the tenant, I am still responsible for any damage done to the unit by my animals, whether or not they are prescribed to me. However, what I have read says that any charges are to be assessed upon move out and that no upfront deposits can be charged for companion animals. I guess this is why I am wondering whether I can get the deposit back now, not because I would try to shirk responsibility for any damage done (which, for the record, there hasn't been any).
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