Assuming you're in the U.S., I'm afraid that won't accomplish a single thing. (And even if you're not, I doubt it'll accomplish anything, either.) Your local police have no jurisdiction over an international airline.

I haven't had time even to read this thread in full, let alone research the matter extensively, but has anyone checked to see the time limit for an airline to refund a given fare? My educated guess is that it's explicitly stated either in the fine print of AA's own paperwork -- though not necessarily in the fine print you'd typically see describing conditions for a given fare -- or somewhere in the DOT's airline rules & regs.

In any event, I'd recommend that everybody who hasn't yet received a refund contact their CC company and file a refund claim. AA may not be responding to individuals, but responding to thousands of requests from AmEx or any major credit card issuer is another matter entirely. (And if your CC company receives *no* response from AA within a certain period of time -- no, I'm afraid I don't know the length of said period, or if it varies depending on the card -- they should automatically reverse the charge and refund your money.)