  The purpose of this work is to determine the location and stability of the
Cassini states of a celestial body with an inviscid fluid core surrounded by a
perfectly rigid mantle. Both situations where the rotation speed is either
non-resonant or trapped in a p:1 spin-orbit resonance where p is a half integer
are addressed. The rotation dynamics is described by the Poincar\'e-Hough model
which assumes a simple motion of the core. The problem is written in a
non-canonical Hamiltonian formalism. The secular evolution is obtained without
any truncation in obliquity, eccentricity nor inclination. The condition for
the body to be in a Cassini state is written as a set of two equations whose
unknowns are the mantle obliquity and the tilt angle of the core spin-axis.
Solving the system with Mercury's physical and orbital parameters leads to a
maximum of 16 different equilibrium configurations, half of them being
spectrally stable. In most of these solutions the core is highly tilted with
respect to the mantle. The model is also applied to Io and the Moon.
