I would start by being polite. Sending a certified letter, return receipt requested is the polite implied threat. No need to make it explicit -- the chief will understand the implication.
What implied threat? That you'll complain some more? The deadline in the law has no teeth, the CoP doesn't care, there are no repercussions to him even if it goes to court. Heck, the local politicians will probably praise him for making getting an LTC harder
Follow
@Len-2A Training advice, a polite letter and talk to those who can be of help. You goal is to get the LTC NOT fix the BS, or is your goal to be the example that goes to court and doesn't see their LTC for years if ever?
OP BTW you don't say who gave you that status, I assume it was the state by the wording. If that's true, then it was sent to the state and they did the checks, and then it goes back to the local PD where they get final say (suitability, I guess they could correct a mistake). This is where most PDs insert their arbitrary delays. But if the PD OKs it then the state prints it and mails it to the PD. Who may sit on it some more, but then it goes to you. They only need to claim "he displayed clearly aggressive behaviour when interacting with police officers" You know, implied threats.
Keep in mind the local PD can kill your app at any point based on suitability. Go ahead as say SCOTUS and the law says, the reality is the PDs can and do deny as unsuitable outside of what the law technically allows and the district courts will support them. You may win in the long run, but thats time and money.
BTW the state sending it back to the locals pending approval, does not say the state approved it, only that the sent it back. It could have gone back as ineligible. And yes they would definitely play this game, they don't want to get into a discussion with you about it, let the locals deal with it. Not saying it was denied, just saying you don't know yet.