Grounded vs. Hot
Check your manuals first. Don't tell my wife I said this, but I think I was wrong.
I was speaking from memory, and way back when in-car monitors were practically unheard of, I beleive there was at least one that had the parking brake lead that went to the actually brake circuit, so that when the indicator light was on on the dash, the circuit was activated and you could watch the monitor.
anyway, just check to see what the manual says (+12V vs Grd).
Also, glad you do have saety as your first thought. No offense meant Defaiantguy, but "Screw the cops, you bought this monitor for you, not your passengers," is a pretty... immature (best word I could think of) way of thinking. Cops are smarter than that. If he sees you watching TV or playing a game, he won't be fooled by you switching it over quickly to an audio screen.