Gwinnett County police said the man has since been identified as Serafin Gutierrez-Carvajal, 33, and is wanted on charges of sudden snatching and possession of cocaine, The Atlanta Journal-Constitution reported Friday.
Gutierrez-Carvajal, who goes by the name "Sarah," allegedly accosted a woman Dec. 20 as she was walking toward her vehicle outside a supermarket in Norcross.
Police said he pushed her, took her purse off her shoulder and fled on foot.
The woman told authorities she recognized the robber as a neighbor she knew as "Sarah."
During a search of Gutierrez-Carvajal's residence, officers found several small bags of cocaine and arrested two of his roommates, Franciso Javier Velasco-Bautista, 32, and Claudia Gomez-Perez, 32.
Both are being held at the Gwinnett County jail on suspicion of immigration violations.