  In this article, we state the Bohr-Sommerfeld conditions around a singular
value of hyperbolic type of the principal symbol of a self-adjoint
semiclassical Toeplitz operator on a compact connected K\"{a}hler surface.
These conditions allow the description of the spectrum of the operator in a
fixed size neighbourhood of the singularity. We provide numerical computations
for three examples, each associated to a different topology.
