I think you are missing a few key points...

You will probably find that your municipality lawyers and/or insurance brokers will require a flight ops department to be setup and run much like 135 operation (formal screening, training, and checking with recurrent training/checking). You will almost certainly need a CPL...LE agencies are NOT in any way exempt from the FAR's so you cannot fly in support of your job (ie be compensated while flying) without a CPL and a 2C medical. A LS or PPL and drivers license will not cut it.


If it's a small agency and all they can afford is an LSA and one pilot (you), you will still probably need to find an outside mechanism to perform independent pilot QA (flight safety, or another contract flight training outfit)


I think this is going to be harder than you think. First step will be to get the concept and budget approved, not start your personal flight training.