You can obtain the records from the state library in Richmond - 800 E. Broad Street. You don't have to prove you're a relative since the records are over 75 years old. Eastern State doesn't have the records there, but they might have her patient card when she was admitted. They will mail you a copy of the patient card if they have it. Email a request and give your mailing address to:
Lea.Brunson@DBHDS.virginia.gov
She works at the hospital in Williamsburg. Wait to get the card before you go to the library to research. When she sent me my grandmother's, she also included information on where to look in the library archives for her specific records. Hope this helps!