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??

i tink it is possible.
Imagine a small insect on the surface of a lake. the incident from the
insect on the suface of water is refracted in all directions
symmetricall so that light will be there every where. But all fish are
not able to see because they can see only at critical angle.

No.  A condition for total internal reflection (the phenomenon you are
describing) is that the light ray must be propagating from a medium of
higher refractive index to a medium with lower refractive index.

See http://www.glenbrook.k12.il.us/gbssci/phys/Class/refrn/u14l3b.html

The phenomenon of total internal refraction takes place when light
travels from optically denser medium to optically rarer medium. Hence,
light rays coming from air to water will certainly enter the water
surface no matter what the angle is.

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