I have a Samsung GALAXY S3 with a rooted Android 4.1.2. My network provider is AT&T.
I tried dialing
*#7465625# but it doesn't work:
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You could try an app to do this, Samsung have removed/changed some of the Dialer codes on the Galaxy range.
GalaxSim Unlock seems to do what you want, it checks if SIM locked, and offers an in-app purchase to SIM unlock. Please note I have not tested this app.
You could also pop in a SIM from a friend's device that is on another network and that should tell you pretty quick!
To use this method you need to update your S3 to 4.1.1 Jelly Bean which was released on December 3, 2013 by Samsung:
(I personally don't have the  NW Lock NV Data INITIALLIZ, but I guess it might help others)