  We investigate the appearance of resonances in three-body systems using
pionless effective field theory at leading order. The Faddeev equation is
analytically continued to the unphysical sheet adjacent to the positive real
energy axis using a contour rotation. We consider both, the three-boson system
and the three-neutron system. For the former, we calculate the trajectory of
Borromean three-body Efimov states turning into resonances as they cross the
three-body threshold. For the latter, we find no sign of three-body resonances
or virtual states at leading order. This result is validated by exploring the
level structure of three-body states in a finite volume approach.
