In this particular situation (with the bicyclist), you first pay a visit to the police department in question, with a copy of the video in hand, present the situation to whoever is at the front desk, and ask them NICELY what they plan to do about it and how to proceed. It may turn out that given the situation, the police department will want to make this situation go away without having to go to court. (It would be best for all parties concerned, and I would say that this is likely.)
If you get brushed off, THEN you consult with a lawyer concerning how to proceed.
Suing the police is exceedingly difficult. Their job involves going to court. They know how to present cases; it's their job. They also know what evidence to present and how to answer questions, and they can make your life miserable if they want to. Do not attempt it without legal advice.
I tend to suspect that in a case like this, it will not be necessary. They know they screwed up, they know the evidence is out there, and it's less expensive by far to settle the case first and NOT go to court.