Women didn't start to get jobs in the police force until the late 19th century to early 20th century. But in fiction, female characters broke into the sleuthing business much earlier.
Our image of the early detective fiction is dominated by blokes: from Sherlock Holmes in England to Di Renjie in China, whose work as a magistrate in the Tang Dynasty comes to Anglophone readers via 18th century Dutch diplomat Robert van Gulik (and last year through the Hong Kong cinema blockbuster Detective Dee, which I'm still waiting to watch and features a subplot about China's "first female empress").
Women detectives were solving crimes almost from the beginning of the genre, but following the clues to find the first female sleuth in fiction is a more difficult job than you might imagine, with a surprising array of contradictory claims to the title. Plenty of sources online wrongly cite The Experiences of a Lady Detective by British author Andrew Forrester, from 1864.
But after traveling down the rabbit hole of Google-based research, I also found mention of a book by Catherine Crewe called The Adventures of Susan Hopley, or Circumstantial Evidence, published in 1841, months before Edgar Allen Poe's short story "The Murders in the Rue Morgue" came out, which is frequently cited as the birth of detective fiction.
An essay by Lucy Sussex clued me in to Susan Hopley, although actually Sussex argues that Emily in The Mysteries of Udolpho is an even earlier "proto female sleuth." The classic Gothic novel, Sussex writes, has a structural role "comparable to that of the detective, being a rational elucidator of the mysteries of the castle, which includes searching for traces of crime".
Any excuse to re-read Ann Radcliffe, frankly, is good enough for me, but by the time we get to Catherine Crewe's novel, all ambivalence about whether the characters "really count" as detectives seems to be over. Susan Hopley features not one but three female detective characters, focusing mainly on the story of Susan, who is—guess what?—a maid. A big contrast to later generations of detective characters, who have often tended to be members of the upper classes. (You can read the novel online for free.)
Dante Gabriel Rossetti drew the illustrations for one edition of the novel, which was a bestseller in its day, although some of the odd dimensions suggest to me he may have been referring to the dodgy theory that criminals could be detected by studying their head shape:
Was the dog a suspect?!
There may well be earlier female detectives in fiction, particularly in languages other than English, but this is the most ancient example I could find.
Turning to more modern mediums, such as film, some of the early female detective characters include Torchy Bane in Smart Blonde:
On television, in the US you had Honey West (Anne Francis) in the 1960s, who claims the title of the first female detective to star in a regular series. She had an ocelot and a convertible, naturally:
Of course, in the UK we had the wonderful Avengers, which starred first Honor Blackman as Cathy Gale, alongside Steed, and then later Emma Peel (Diana Rigg):
Get Christie Love! brought us the first or one of the first black female detectives on television:
Teresa Graves was also the first African American woman to star in an hour-long TV series.
(Somewhere in the transition from Torchy Blane in the 1930s to Christie, Emma and Honey, body suits became essential wear for female detectives..)
Have I missed out any other firsts? Which early female detective characters do you love?