Green’s Dictionary of Slang

(US) a drunken woman; by implication a prostitute.

1909

J. Ware Passing Eng. of the Victorian Era 194/2: Perfect lady (Street). Not at all one – anything but. Satirically applied to any woman drunk and misbehaving herself in the streets. The phrase took its rise from a police court case, in which a witness deposed that, though the prisoner did get her living in the streets and dram a little, she was otherwise a ‘perfect lady’.