There were indeed some slaves owned by the various governments of the United States. There were never very many of them, since most slaves were on plantations and plantations were not owned by the government, but they did exist. These slaves mostly did janitorial duties. Cleaning up the public buildings and generally looking after the politicians. They also did some public works. In New Orleans, for example, they helped keep the streets clean and build roads and bridges. Slaves in New Amsterdam actually did work on the docks and they were owned by the colonial government, though that was before the United States existed, of course. Unfortunately, I'm not aware of a serious study of government owned slaves. There are some newspaper documents from the New Orleans area that I have run across where state owned slaves ran away and the state wanted them back. That was in the Natchez Courier, which carried a lot of runaway slave advertisements from Louisiana.

One source comes to mind. Judith Schaffer, Becoming Free, Remaining Free. She mentions it briefly, but doesn't go into much detail as far as I recall.

This subject raises an interesting question about escheat—the passing to the state of property owned by a person who left no will or descendents. Here are some interesting documents concerning slaves escheated to the University of North Carolina.

The few sources I find online don't show such an occurrence, but it seems quite likely that during the century when slavery was legal in many states, they—like any other property—would have escheated to the state and been sold as soon as practicable.

Like collective slave ownership?