  We prove a local unique continuation result for Schr\''odinger operators with
time independent Lipschitz metrics and lower order terms which are Gevrey 2 in
time and bounded in space. This implies global unique continuation from any
open set in a connected Riemannian manifold. These results relax in the same
geometric setting the analyticity assumption in time of the
Tataru-Robbiano-Zuily-H\''ormander theorem for these operators. The proof is
based on (i) a Tataru-Robbiano-Zuily-H\''ormander type Carleman estimate with a
nonlocal weight adapted to the anisotropy of the Schr\''odinger operator and
(ii) the description of the conjugation of the Schr\''odinger operator with
Gevrey coefficients by this nonlocal weight.
