A few of the high-performance cars used for roads policing or VIP protection may be automatics simply because a manual version of the chosen car does not exist.
UK Police cars are almost always manual transmission. Mostly because they're cheaper to buy and simpler to maintain when they go wrong.
The balance is likely to tip in favour of automatics now that they can achieve better mpg figures than manuals and because modern dual mass flywheels ensure that clutch replacements often cost three or four times more than they used to. Some manufacturers are now also starting to offer "free" upgrades to automatic (in reality it still normally means "less discount from list prices") or even offering auto as the standard default option with manual at extra cost.
Police cars in the UK have automatic transmissions.