It does not depends upon the crystal structure, it will depend upon nature of material. We should know about the nature of material first instead dielectric constant.
The dielectric constant varies for material to materials. But not exactly on the crystal structure. Suppose if you take BT, it has different crystal structure while heating.
Please read some research papers thoroughly to get more information.
First of all, please define the type of material with which you are working: with polymers/organic compounds or with inorganic materials? If you are working with inorganic materials you can read my work and some relevant works, in which the nature of electric processes and relaxations are described for this type of materials.
Article Electrical Conduction Mechanism and Dielectric Properties of...