The weather station will send a special code that will
override the CB channel or even turn on the radio if it's turned off
to recieve the weather emergency.
So far I've only found 2 models of CB radios with weather alert.
One from Uniden, the other from Cobra and they both look very similar.

The old style of alert was a 10 second 1050 HZ tone. The new style
of alert is called SAME (Specific Area Message Encoding).

http://www.nws.noaa.gov/nwr/
http://www.nws.noaa.gov/nwr/nwrrcvr.htm