Counting prisoners in the census

[Nebuchadnezzar]

In Hamilton County Ohio we have the Hamilton County Jail and the prison in this area is in Lebonon Ohio.

I think it's that way for most of the state prison systems but I'm not sure.

EDIT: I just looked up Rikers Island and they classify it as a jail, not a prison but the info comes from Wikipedia so take it for what it's worth.