  We determine the restriction of Weil representations of unitary groups to
maximal tori. In the local case, we show that the Weil representation contains
a pair of compatible characters if and only if a root number condition holds.
In the global case, we show that a tori period corresponding to a maximal
anisotropic torus of the global theta lift of a character does not vanish if
and only if the local condition is satisfied everywhere and a central value of
an $L$-function does not vanish. Our proof makes use of the seesaw argument and
of the well-known theta lifting results from $\operatorname{U}\left(1\right)$
to $\operatorname{U}\left(1\right)$. Our results are used in other papers to
construct Arthur packets for $G_2$.
