I want to release read & write permission to a non root user
What I think this means is that currently only root can read/write but you want another user (who is a member of admin_usr) to be able to?
In which case the above (chgrp) will still retain the existing permissions on the file (ie, 644). You will need to:
chmod 664 FILENAME
chmod g+rw FILENAME
so that the group has rw.