In a civil suit between the two drivers, the police are not a party to the case. What that means is that a simple discovery request to the opposing side obviously won’t work. Thus, the party seeking the video would have to subpoena the police for it. If the police have privacy grounds on which to refuse to comply with a subpoena to hand over the video then you can bet they would have grounds to refuse to disclose the video in a public records request. Generally speaking a party to a court case can get records by subpoena that he could not get via a public records request but it typically would not work the other way around: one wouldn’t get with a public records request something that could not be obtained by subpoena. If the police refuse to release the video after being served a subpoena, then a motion to compel may be filed with the court and the judge will decide the matter.

