I just read the Woman in Red's first and subsequent appearances in Thrilling Comics, and the following introduction paragraph is simply in error:
"Frustrated by the limitations of her job, policewoman Peggy Allen creates a secret identity. As the Woman In Red, she wears a red floor-length coat, a hood, and a mask. Her detective and firearm skills help the Woman in Red accomplish her crime-fighting goals without the restrictions imposed on everyday police officers. During her vigilante career, the Woman in Red battled villains such as the Black Death and Voa."
Pegg Allen is, in fact, the police chief's best undercover agent and she is assigned to all her cases by him. Usually as a nurse or maid, she infiltrates the crime scene. To keep witnesses from suspecting the new maid, she adopts the Woman in Red identity. All of this is known to her boss, who calls her "Peggy" while she is in costume and congratulates her in her work, in his office, after each case.
She is not a vigilante, nor is she "frustrated by the limitations of her job." She is, in fact, a recognized asset to the police force, praised by her superiors who know of her use of the Woman in Red disguise.