Green’s Dictionary of Slang

merry-go-round v.

(US Und.) of a prisoner, to clear all administrative and bureaucratic procedures before being discharged from prison at the end of a sentence.

[US]Bentley & Corbett Prison Sl. 8: Merry-Go-Round Before an inmate can leave a prison he must clear all the various agencies within the institution, such as the library and recreation department. This is to insure the inmate is not in possession of any items from these agencies.
[US]J. Hannaham Didn’t Nobody Give a Shit 39: The day of, after the merry-go-round — as they dubbed the offloading process.