Here in Thailand police mostly get around on 100 & 125 step-thrus. I think they are mostly their own bikes. You see the odd Harley and other big bike ridden by a police officer. There are some department owned bikes kitted out police style, including a large number of the 200cc Tiger Boxer (a small Thai manufacturer). I have also seen a few of the previous CBR150 model, but none of the current model yet. They have a few police BMWs, and maybe other big bikes, which are mainly used for ceremonial purposes.
Police here do not bother with chasing speedsters or other moving violators. They prefer set up checkpoints where motorcyclists sans helmet, licence, current registration, and even the odd drunk obligingly stop to be booked. They usually cough up a "fine" on the spot, sometimes with a ticket being issued, sometimes without. Foreign tourists, and teenagers are big contributors. Car owners seldom have time to stop.