Dear Ms. Kintscher,
Thank you for posting your request on History Hub!
Birth Certificates are typically considered Vital Records. These records are created by local authorities, and with possible exceptions for events overseas, in the military, or in the District of Columbia. They are not considered Federal records; therefore they are not held by NARA.
We suggest that you contact the NYC Health Department Office of Vital Records to request a search for Katherine Washington’s birth certificate. To make ordering easier they have a website that you can use to request certificates online: NYC Birth Certificates. You may wish to note any name variants or broaden your search for the surrounding years. In addition, the FamilySearch Research wiki for [How to Find United States Vital Records] may be helpful.
We hope this is helpful. Best of luck with your family research!
Most records seem to indicate that she was born in 1914 (age listed in censuses etc) probably in September or October. I could find no births of females named Washington born in NYC during that time period, but there is one female born 20 Sept 1914 with the surname Walker born in Manhattan.
You would have to decide if it is worth purchasing this birth certificate to see who the mother (or parents) were.