  Inspired by the work of Z. Lu and G. Tian [21] in the compact setting, in
this paper we address the problem of studying the Szeg\"o kernel of the disk
bundle over a noncompact K\"ahler manifold. In particular we compute the
Szeg\"o kernel of the disk bundle over a Cartan-Hartogs domain based on a
bounded symmetric domain. The main ingredients in our analysis are the fact
that every Cartan-Hartogs domain can be viewed as an "iterated" disk bundle
over its base and the the ideas given in [4] for the computation of the Szeg\"o
kernel of the disk bundle over an Herimitian symmetric space of compact type.
