The correct color is scarlet, not pink, so "A Study in Scarlet" It is 100% correct. The author Sir Arthur Conan Doyle was native English speaker and highly educated. "study on" and "of " are used also : This book is an excellent study of/on the origins of philosophy. It is a play on words, because scarlet/red is symbolic of communism, which is one of the themes in the book. Scarlet is also the color of blood, so it is symbolic of studying murder. I can't remember if this is also a play on words in this case: A study is also the name of a room in a house, so it could also mean the room was red. A painting could be called "A Study in Blue" meaning it is examining aspects of the color, and for that use I usually see "in" used. Using "study" this way has become old fashioned.

The usage of "study in something" is literary or found in high-level journalism, in my experience. This is my own example of how I've seen it used: "When he heard the bad news, his face was a study in bewilderment." This means that he was so bewildered (astonished) that you could study the concept of bewilderment by studying his face. Here is an example from time.com : "On the basketball court or soccer field, he is a study in gravity-defying grace."

I think my guess is confirmed by the actual text, online at http://www.gutenberg.org/files/244/244-h/244-h.htm in which Sherlock Holmes calls it "art jargon:" "I must thank you for it all. I might not have gone but for you, and so have missed the finest study I ever came across: a study in scarlet, eh? Why shouldn't we use a little art jargon. There's the scarlet thread of murder running through the colourless skein of life, and our duty is to unravel it, and isolate it, and expose every inch of it. And now for lunch, and then for Norman Neruda. Her attack and her bowing are splendid. What's that little thing of Chopin's she plays so magnificently: Tra-la-la-lira-lira-lay." Now, as to why artists use that terminology, I don't know.

A "study in something" is a perfect and complete example of something. It is the beginning of a phrasal noun (multiple words together that form a single meaning). Whatever is described right after it becomes of the part of the noun. Some examples: That English class was a study in suffering. Meaning: It was really, really painful. The perfect example of what suffering feels like. "study in suffering" are three words that form a single noun that represents that perfect example. And for the record, "Study in Pink" is the title of a show (the book it's based on is "Study in Scarlet" which is more of a dark red color). --- "Study of" and "Study on" are pretty close to the same meaning. Usually it means someone is either writing a paper or conducting scientific tests to understand something better. Examples: "I am doing a study on curing cancer in mice" "I am doing a study of how people respond to loud noises" In these cases, "of" and "on" are prepositions and totally separate from the word "study"

I think the terminology comes from oil painting. An oil painting--of any subject--that is a sort of exercise in the use of shades of a single color is called "a study in [color name]." Notice that an artist's workplace is called "a studio." (There is a similar kind of word use in music, where certain pieces of music that emphasize some point of technique are called "étude.") The Sherlock Holmes novel sounds at first sounds cold, factual, and unemotional. Then we realize that "scarlet" is the color name traditionally used to describe the color of arterial blood.