Are the Case-Shiller® Home Price Indexes expressed in real or nominal values?
The Case-Shiller® Home Price Indexes (CSI) are expressed in nominal terms. This includes the two historical datasets ("Raw" and "Square") and the Moody's Analytics forecasts.
Because the data are price indexes, they already represent inflation (albeit in a very specific sector: single-family homes with repeated arms-length sales). Deflating the numbers further would be of dubious utility. You might seek to separate "input costs" and "irrational exuberance" but we cannot recommend a CPI or deflator time series that would do this.
You can, however, compare the CSI to other measures of inflation on Data Buffet, such as the BLS CPI-U or CPI-W (all-items, core, or housing), or the Moody's Analytics-estimated CPI-U for all metro areas.
CoreLogic® Case-Shiller® Home Price Indexes
CoreLogic Case-Shiller House Price Index Forecast