  We consider self-dual transverse-field Ising spin chains with $m$-spin
interaction, where the phase transition is of second and first order, for m <=
3 and m>3, respectively. We present a statistical analysis of the spectra of
the Hamiltonians on relatively large L <= 18 finite lattices. Outside the
critical point we found level repulsion close to the Wigner distribution and
the same rigidity as for the Gaussian Orthogonal Ensemble. At the transition
point the level statistics in the self-dual sector is shown to be the
superposition of two independent Wigner distributions. This is explained by the
existence of an extra symmetry, which is connected to level crossing in the
thermodynamic limit. Our study has given no evidence for the possible
integrability of the models for m>2, even at the transition point.
