Origin and history of shamus

late 12c., sloth, "track or trail of a person or beast," from Old Norse sloð "trail or track," as of a person in snow, a word of uncertain origin.

The meaning "detective" (1872) likely is ultimately a shortening of sleuth-hound "keen investigator" (by 1846). This is a figurative use of that word, which is attested from late 14c. in its original sense of "bloodhound," noted early 19c. as a Scotticism. The extension to police detectives would be from the notion of a relentless pursuer.

Sleuth alone as a name for "a detective" is attested from 1872 in sensational New York magazine stories featuring or credited to "Old Sleuth" the detective. (Sleuth also was the pseudonym of a Brooklyn newspaper correspondent active earlier in 1872.)

A "Richard Sleuth" is the main character in a sensational novel serialized in England in 1865 and published in 1866 as "Bound to the Wheel," by John Saunders. Richard Sleuth is not a detective but a relentless immoral schemer "physically a coward but intellectually cool, who pursues base ends by base means" according to a contemporary reviewer. Perhaps the character-name is based on sleuth-hound. The U.S. journalistic use six years later might be aware of Saunders's novel.

The series of U.S. crime-thriller stories and cheap novels continued popular through the 1880s and '90s, and the use of sleuth for “detective” in titles was a subject of a lawsuit among publishers. Compare hawkshaw, Sherlock, shamus.