The Bureau of Justice Statistics has posted a report on Suicide and Homicide in State Prisons and Local Jails. Some of the key facts regarding this topic can be seen here. The overall homicide rate can be seen here for comparison. The suicide rate information, for the United States in General, can be found at the WHO site. The WHO site only list 1999 and doesn't do comparisons, but you can compare the rate to 1999 in prisons and jails.
Needless to say, suicide rates are higher in jails than in the general populace.