Rays of light in water that shine up to the water -air boundary at
angles of more than 48 degrees to the normal are totally reflected. 
No rays beyond 48 degrees refract outside.  How about the other way
around?  Is there an angle at which light rays in air meeting the air-
water boundary will reflect totally or will some light be refracted at
all angles?

This is to do with the relative permiability of the two materials.

There is no angle that will reflect all light.

The relevant physics is Snell's Law.  See for example, 

http://buphy.bu.edu/py106/notes/Refraction.html

Light rays originating in the air at a razor-thin glacing angle to the
water's surface would follow the same path (in reverse of course) as
those originating in the water and exiting at the same glancing angle
to the surface (in your example, at 48 degrees).  Thus all the
external light, once it enters the water, shall be found with a cone
48 degrees to the normal to the surface.  Light originating in the
water, at an angle less steep than this, as you've noted, is totally
reflected within the water.