The Secret Life of Anna Blanc

It's 1907 Los Angeles. Mischievous socialite Anna Blanc is the kind of young woman who devours purloined crime novels but must disguise them behind covers of more domestically-appropriate reading. She could match wits with Sherlock Holmes, but in her world women are not allowed to hunt criminals.
Determined to break free of the era's rigid social roles, Anna buys off the chaperone assigned by her domineering father and, using an alias, takes a job as a police matron with the Los Angeles Police Department. There she discovers a string of brothel murders, which the cops are unwilling to investigate. Seizing her one chance to solve a crime, she takes on the investigation herself.
If the police find out, she'll get fired; if her father finds out, he'll disown her; and if her fiance finds out, he'll cancel the wedding and stop pouring money into her father's collapsing bank. Midway into her investigation, the police chief's son, Joe Singer, learns her true identity. And shortly thereafter she learns about blackmail.
Anna must choose either hunt the villain and risk losing her father, fiance, and wealth, or abandon her dream and leave the killer on the loose."