This means underhand or unscrupulous behaviour or trickery. There is doubtless no more activity of this kind in the USA than anywhere else, but it was in that country that the word was coined, sometime in the 1860s. The first recorded instance appeared in 1867 in Beyond the Mississippi by Albert D Richardson: “From Minnesota had been imported the mysterious term ‘scull-duggery’, used to signify political or other trickery”. (Do I detect a hint of “These Minnesotans, you know how they are ...”?)
The word was still mysterious a few years later. One of its very early sightings is in this splendid political exchange, which I have gleaned from the Official Report of the Proceedings and Debates of the Third Constitutional Convention of Ohio, 1873-1874:
Mr. WEST. It is urged upon the assumption that there has been what some gentlemen here have characterized as “smouzling”.
Mr. HOADLY. What is that?
Mr. WEST. Skulduggery.
Mr. HOADLY. Well, what does that mean?
Mr. WEST. I do not know what it means, but that is what I heard talked about here.
We are hardly the wiser as a result, except that the members of the Ohio legislature didn’t know what skulduggery meant, except that it was something that could be considered vaguely disreputable. Skulduggery seems to have caught on in the US quite slowly, and was imported into Britain only much later.
Though we now know pretty well what it means, its origin remains unclear. Experts think that it is probably Scots, most likely from sculduddery. In the eighteenth century, sculduddery meant fornication, adultery, unchastity. In the nineteenth century it seems to have shifted to a sense of obscenity and indecency in language. Later it was respelled and changed again to its current meaning. Unfortunately, nobody seems to have the slightest idea where sculduddery comes from, so here the trail runs into the sand.