The noun Dickless Tracy, also dickless Tracy, designates a female police officer or a female traffic warden. This noun puns on:
– the noun dick, slang for a man’s penis;
– the name of Dick Tracy, a comic-strip detective created in 1931 by the U.S. cartoonist Chester Gould (1900-1985).

—Cf. also ‘in more trouble than Speed Gordon’: meaning and origin.

The noun Dickless Tracy perhaps contemptuously suggests that a woman cannot be as effective as a man.

The following is from Cop Talk: A Dictionary of Police Slang (Lincoln (NE): Writers Club Press, 2000), by Lewis J. Poteet and Aaron C. Poteet:

Dickless Tracy—a woman policeperson. Derived from the comic strip detective Dick Tracy, this term is not only sexist but seems to suggest that the original, Dick Tracy himself, had a macho which somehow escaped his readers; he seemed sexless, like Clark Kent (“Clark Bent”).

These are, in chronological order, the earliest occurrences of the noun Dickless Tracy that I have found:

1-: As a humorous nickname—from The Twelfth Step (New York: Charles Scribner’s Sons, 1957), by ‘Thomas Randall’:

“Shhh!” Evelyn whispered. “Not a word. It’s the sinister Mr. Bumstead and I’m Dickless Tracy.”
[…]
“Dickless Tracy,” she repeated. “Where did you ever hear that?”

Note: This book contains the earliest known use of the adjective dickless, meaning having no penis, hence, figuratively, impotent; powerless, weak.

2-: From The American Language (London: Routledge and Kegan Paul, 1963)—as quoted in the Oxford English Dictionary (3^rd edition, 2019):

Dickless Tracy, a policewoman.

3-: From the satirical newspaper King’s Cross Whisper (Sydney, New South Wales, Australia), No. 34, 1967—as quoted by Gerald Alfred Wilkes (1927-2020) in A Dictionary of Australian Colloquialisms (Sydney University Press in association with Oxford University Press Australia, 1990):

Dickless Tracy: A woman policeman.

4-: From the account of Attack on Mormondom, a speech delivered by Dr. Fred Hagen, University professor of philosophy, published in The Daily Utah Chronicle (Salt Lake City, Utah, USA) of Wednesday 17^th January 1973:

The greatest criticism raised by Dr. Hagen of the Mormon church […] was that “the sovereign state of Utah is treated as a Mormon country club.” This is evident, he stated, in such overt measures as the legislation concerning vasectomy, liquor, and pornography. Further, stated Dr. Hagen, covert measures such as the entrapment of men looking for prostitutes by meter maids or “dickless Tracys” show the tendency for the “faithful” to use any means to legislate morals.

5-: From Herb Caen’s column Just Foolin’ Around, published in the San Francisco Chronicle (San Francisco, California, USA) of Monday 7^th June 1982:

NO PLACE TO hide: Lake County’s very first traffic light has been installed on Highway 53, at the road leading into Clearlake. However, that blessed county still does not have a single parking meter . . . The good old days, reminisces Richard Hart, were when the meter maid would say “Move along, buddy,” instead of blocking your car with her Ill Humor truck and writing a $40 ticket . . . Police Chief Con Murphy thinks some of us are too hard on what he calls “traffic controllers” and Judith Whipple calls “Parky Pigs” (hold those Dickless Tracy letters—old joke and very bad). If you don’t like the parking laws, he says, go change them. Simple enough. And he keeps insisting that the number of citations being written is actually decreasing.

6-: As a humorous nickname—from Valentine Love Lines, published in the Herald and Review (Decatur, Illinois, USA) of Monday 14^th February 1983:

Donnie Bear (Master)

Thank you for releasing my chains long enough to write this—oh my, but what fun we do have. I know you think you’re my boss. Without you I would be lost. I know you think you’re my lover but Buddy I’ll always have you under cover. Will love and keep you always. (357 Mag)

Your wife (NMR)
Better known as Dickless Tracy.

7-: From an article by Susan Hely about Sue Mangan, a twenty-year-old police constable, published in The Sydney Morning Herald (Sydney, New South Wales, Australia) of Saturday 4^th February 1984—Darlinghurst is a suburb of Sydney:

Mangan is one of 18 policewomen at Darlinghurst (out of 136 police) whom one sergeant calls Dickless Tracys. She has been on general duties at Darlinghurst for two years.

8-: From Racist slang is no joke to recipients, by Peter White, Ethnic Affairs Reporter, published in The Sydney Morning Herald (Sydney, New South Wales, Australia) of Friday 7^th December 1984:

Fourth generation Chinese-Australian Vic Lee is happy for the police to call him a “gook, a chow, a chink or a slopehead”, and he has no objection to them calling his friends “wogs, chocolates, coconuts or even boongs”.
But that is with the proviso that the police raise no objection if he addresses them as “pig”.
Yesterday the Herald interviewed ordinary Australians with non-Anglo-Saxon backgrounds about remarks on police racism made by the NSW police ethnic liaison officer, Inspector Les Thorgood, in yesterday’s paper.
We spoke to Australians of Greek, Kampuchean, Chinese, Cypriot, Spanish, Lebanese, Malaysian and Indonesian descent.
The large majority were outraged by Inspector Thorgood’s comments that names such as “wog, slopehead and dago” were a convenient way of identifying groups of people and not necessarily racist.
Most rejected outright the idea that the use by police of these names was acceptable in any circumstances.
They felt it would lead to racial hatred and would deny the equality of all Australians whatever their country of origin.
Mr Lee, proprietor of the Kings-grove Dry Cleaners, said: “They can call me those names so long as I’ve got the right to call them by the common slang names which everyone knows which are flatfoot, or walloper, or bull, or pig.
“I mean all Australians should be able to use common slang back to them, but how would you like to walk up to a policewoman and say ‘hey there dickless Tracy’. . . it’s just not on.”