We study the solutions of the Dirac equation in the background of the Nutku helicoid metric. This metric has curvature singularities, which necessitates imposing a boundary to exclude this point. We use the Atiyah-Patodi-Singer [Math. Proc. Cambridge Philos. Soc. 77, 43 (1975)] nonlocal spectral boundary conditions for both the four and the five dimensional manifolds. (c) 2007 American Institute of Physics.