Can A Shelter Deny Releasing Health Records After Adoption?

New York residents involved here, I work in a vet clinic myself and I'm trying to help one of our clients figure out what even is going on with this situation. The shelter in question is apparently refusing to release health records until after she's gotten a spay for her new pet, which are including rabies and DHPP vaccinations which we need records of before we can even perform a spay for this poor woman.

I'm about to call them later today and request them on her behalf but any back up for legal grounds would be helpful!

Quick edit to add:

She's got an appointment with us soon to establish her as a client and create the client patient doctor relationship, but had an appointment last month for the same that unfortunately needed rescheduling for unrelated reasons. If that's relevant at all, I thought it may have so there's