As said above, here is some more precise reference:
Originally Posted by EU-OPS 1.297
Planning minima for a take-off alternate aerodrome. An operator shall only select an aerodrome as a take-off alternate aerodrome when the appropriate weather reports or forecasts or any combination thereof indicate that, during a period commencing one hour before and ending one hour after the estimated time of arrival at the aerodrome, the weather conditions will be at or above the applicable landing minima specified in accordance with OPS 1.225. The ceiling must be taken into account when the only approaches available are non-precision and/or circling approaches. Any limitation related to one-engine-inoperative operations must be taken into account.
Having said that, some CAT II/III airlines restrict take-off alternate WX to be above CAT I even if it has CAT II/III RWY.