LEOSA is a Federal Law. It does allow a few state restrictions that are written into the law such as gun-free safety zones where carry is restricted. It does not allow states to define the type of firearm or ammunition you can carry. Those are specifically covered in the LEOSA statute so one state cannot require you to qualify with a revolver and a semi-automatic to carry each while another state does not. The question is what is the Federal definition of "type" of firearm. I will have to find it but I have read that the courts have ruled that "type" means handgun rather than a long gun. IF this is true that qualifying with any handgun qualifies with every handgun. Whatever the answer, it is the answer for every state.