As of today, EASA has not issued any Certification Specification for gyroplanes.
EASA recommends to check first the Maximum Take-off Weight of the gyroplane. If it is below 560 kg, national regulation shall be used: indeed, in accordance with the Regulation (EC) 216/2008, Annex I, gyroplanes with a maximum Take-off Weight below 560 kg belong to the ultralight class.
So far there is no gyroplane type certified by EASA. In case of an application for a type certificate of such a product, the EASA would address the certification basis through e.g. Special Conditions in accordance with Part 21.