  We investigate the integrability of natural almost complex structures on the
twistor space of an almost para-quaternionic manifold as well as the
integrability of natural almost paracomplex structures on the reflector space
of an almost para-quaternionic manifold constructed with the help of a
para-quaternionic connection. We show that if there is an integrable structure
it is independent on the para-quaternionic connection. In dimension four, we
express the anti-self-duality condition in terms of the Riemannian Ricci forms
with respect to the associated para-quaternionic structure.
