  Let $X$ be an orientable compact Levi-flat CR manifold and let $L$ be a
positive CR complex line bundle over $X$. We prove that certain microlocal
conjugations of the associated Szeg\H{o} kernel admits an asymptotic expansion
with respect to high powers of $L$. As an application, we give a Szeg\H{o}
kernel proof of the Kodaira type embedding theorem on Levi-flat CR manifolds
due to Ohsawa and Sibony.
