my record still shows the charge but was dismissed.
Are you saying that your record shows that you were charged with the crime but that the charge was dismissed? If so, technically, you have not been convicted of any crime and you should be able to get a permit. It very well may depend on the temperament of the judge but, at least in theory, it should not disqualify you. Just make sure that you show on the application that you were charged for the crime, include all necessary information and go from there.
It would probably also be a good idea to call the issuing authority and ask them your questions.
Still happily answering to the call-sign Peetza.
You do not HAVE a soul. You ARE a soul. You HAVE a body.
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.