Extracting "Crystal Radii" from a CIF file
The CIF file won't contain information on atomic radii, only the positions (in fractional space).

Consider that the atom might be ionic, covalent, etc. so you'll have to choose the atomic radius definition you feel is most appropriate. (Or run some sort of quantum calculation and use the resulting [electron density to define an atomic radius].)

For what it's worth, Open Babel does have a data table of covalent and van der Waals atomic radii, but it sounds like you want something else.