Well ... every carry permit I have ever applied for asks if you have ever been denied a permit in the past or had a permit revoked. At a minimum, getting a BS denial will be a cause for having to explain it from then on.
May issue is what I think you are referring to ...
shall issue statutes say that unless you are a prohibited person, they must (shall) issue you a permit. RI is actually
shall issue in the towns and
may issue with the AG. A little trivia for you: the RI supreme court actually upheld the may issue statute for the AG permits because there was another viable shall issue path to getting a RI permit (that being the town permits).
If you apply and you are denied for a valid reason, you have no recourse, but if they deny you because they don't like the way you filled out the application or for some other reason unsupported by law, then you have every right to sue them. The C.O.P in East Providence has been told by judges on multiple occasions to issue after he had denied permits without cause. I think that if they violate rights knowingly, they should be personally liable, but that isn't the way the law works
CC