  In this article, we state the Bohr-Sommerfeld conditions around a global
minimum of the principal symbol of a self-adjoint semiclassical Toeplitz
operator on a compact connected K\"ahler surface, using an argument of normal
form which is obtained thanks to Fourier integral operators. These conditions
give an asymptotic expansion of the eigenvalues of the operator in a
neighbourhood of fixed size of the singularity. We also recover the usual
Bohr-Sommerfeld conditions away from the critical point. We end by
investigating an example on the two-dimensional torus.
