Perhaps she is listed in the city directories, or perhaps appears in the digitized yearbooks (which include seniors and underclassmen):http://www3.libraryweb.org/lh.aspx?id=1105
When a woman had a baby, it would almost have to be in the state index to births; they are held back by NY for 75 years (i.e. 1938 now). But that index has to be examined in person, as it cannot be NY state law be put online.
If it is a quest to find more about a birth mother, it is difficult as NY is quite restrictive about adoptee information. If it's not, it's still a challenge to find out. Although, an SSDI was found for an Alice St Clair:
Alice M. St. Clair
Last Residence: 14620 Rochester, Monroe, New York, United States of America
Born: 2 Oct 1901
Died: 2 Sep 1987, but you might already have this information.