Generally, you do not have to have a permit to transport a long gun from your home to the appropriate activity (trap shooting, hunting, clays, etc.). You also do not need permit to transport long guns across state lines. Long guns are not "registered" with local agencies. However, most states require that guns and ammo be kept separate when transporting; i.e. gun in the trunk and ammo in passenger compartment.
However, pistols and revolvers are another story. Check with your local police department for those rules.
Rhode Island should have rules on their state web site, either Rhode Island State Police, or the Attorney General.