Just a starter battery? No leisure battery?
If you run dashcam or other devices off a starter battery, without a low-votage cut-off, then eventually the battery will be drained below the voltage at which it can adequately power the starter motor to start the car.
I doubt the police would want their cars to unexpectedly not start, so maybe your car already has a low-voltage cut-off between the battery and the USB port(s). You should look into that. If there's no cut-off, I guess the police counted on the car spending so little time parked that the battery would never have time to be drained before someone started the engine again for a patrol or whatever - but unless you use the car the same way (unlikely, unless maybe it's a company car for a team of security guards or something) you should probably add a cut-off or a leisure/dashcam battery in order to prevent the starter battery from ever getting drained to the point of uselessness. See
https://dashcamtalk.com/battery-discharge-prevention/
Anyway, yes, your Viofo can detect when it has been stationary for a while and can switch into parking mode that way.