I found a copy of 1974's "Man on a Swing" and decided to watch it because it had Lane Smith, Gil Gerard and Tanya Roberts in it. It's an altogether serious movie about police detectives investigating murdered teens.
This movie opens with a one minute-20 second "one take scene" shot by a camera mounted on the police car roof--behind the flashing light bar. It looks like you see the entire drive from the station to the crime scene.
Perhaps some other police movie had a similar opening sequence. But it's clear this movie's opening scene alone would have been sufficient to inspire the comedic version of the same viewpoint that opens "The Naked Gun".
Probably the inspiration for "The Naked Gun" opening sequence
The completely serious film (Man on a Swing) opens with a one minute-20 second scene shot with a camera mounted on the police car roof about a foot behind the flashing light bar. While I am sure it seemed dramatic in 1974, it's impossible to view now without remembering the comedic rendition of the same viewpoint that forms the opening of "The Naked Gun".
While I can't be sure this was the only "cop movie" that had a similar opening sequence, it's pretty clear to me that this film alone would have been sufficient to inspire the Naked Gun spoof scene.