  We discuss a specific class of regular-singular Laplace-type operators with
matrix coefficients. Their zeta determinants were studied by K. Kirsten, P.
Loya and J. Park on the basis of the Contour integral method, with general
boundary conditions at the singularity and Dirichlet boundary conditions at the
regular boundary. We complete the arguments of Kirsten, Loya and Park by
explicitly verifying that the Contour integral method indeed applies in the
regular-singular setup. Further we extend the zeta determinant computations to
generalized Neumann boundary conditions at the regular boundary and apply our
results to Laplacians on a bounded generalized cone with relative ideal
boundary conditions.
