Reading this article on sloths and this article on sleuths* (of the OED kind, discovering a pre-WW1 instance of "omg") made me wonder if the words had anything to do with each other. It turns out that there is in fact a sort of obscure pun here... OED has "sleuth(1) = sloth, laziness" (from "slow-th," also the etym. for "sloth") as well as the more relevant "sleuth(2) = The track or trail of a person or animal" (from Norse "slo(d) = track") -- whence "sleuth-hound" via ellipsis, and eventually the modern sense.
I must say that "sleuth" looks better than it sounds, that sleek and vaguely foreign eu has an effect that's entirely dissipated in the utterance. Neither of the two conceivable pronunciations, roughly "sloofing around" and "slooving around" in my idiolect, is at all suited to the activity.
*via Elisa Gabbert
Addendum didn't realize this immediately but sleuth(2) in its original meaning is cognate with a sense of "slot," which is from the same Norse root.