Here in the US the FAA can impose a type rating on any aircraft it likes (see part 3 below). Generally speaking type ratings are either for big planes or planes that may require additional training for safety reasons.
You can find the full regulations relating to US type ratings in the FAR under
§61.31 Type rating requirements, additional training, and authorization requirements.
(a) Type ratings required. A person who acts as a pilot in command of any of the following aircraft must hold a type rating for that aircraft:
(1) Large aircraft (except lighter-than-air).
(2) Turbojet-powered airplanes.
(3) Other aircraft specified by the Administrator through aircraft type certificate procedures.
In specific relation to the Malibu the US FAA does not require a type rating, you can find a full list of aircraft that require a type rating here. However it should be noted that to fly Pipers M600 and M500 Malibu variants, both of which have a service ceiling over 25,000Ft you would need a High Altitude Endorsement (along with all the other endorsements for a high performance plane like that).
The JAA may require such a rating due to the pressurization system in the plane.