These can be searched online at:
Arizona Department of Health Services, Arizona Genealogy Birth and Death Certificates.
On the same website, Arizona births can be searched for the years of birth 1855 - 1940's.
A disclaimer states: The birth and death certificate images made available on this website do not constitute certified copies.
Find the information you need by calling the library's Infoline at 520.791.4010 or by sending your question to Askalibrarian.