"A surveillance machine with a video camera caught the incident on a tape, which was turned over to the police."
The "which" in here is not clear as to which noun(s) it refers to. It could be:
- the surveillance machine
- the video camera
- the tape
- the incident
- Any combination of the above
In order to be specific, I would write as follows:
- A surveillance........ tape, which machine (or camera, or tape, or incident) was turned over to the police. Or,
- A surveillance.........tape. The machine (or camera, or tape, or incident) was turned over to the police. Or,
- A surveillance.........tape, and the latter was turned over to the police (if only the tape was turned over).
Therefore, the use of the "which clause" is not as simple as it appears. If it is not used properly, it causes more confusion instead of simplifying things.