  We study in this paper the global hypoellipticity property in the Gevrey
category for the generalized twisted Laplacian on forms. Different from the
0-form case, where the twisted Laplacian is a scalar operator, this is a system
of differential operators when acting on forms, each component operator being
elliptic locally and degenerate globally. We obtain here the global
hypoellipticity in anisotropic Gevrey space.
