We present measurements of the near-infrared Calcium II triplet (CaT, CaT*), Paschen (PaT) and Magnesium (MgI) indices for a well-studied sample of 19 bulges of early to intermediate spiral galaxies. We find that both the CaT* and CaT indices decrease with central velocity dispersion (sigma) with small scatter. This dependence is similar to that recently found by Cenarro (2002) for elliptical galaxies, implying an uniform CaT* -- sigma relation that applies to galaxies from ellipticals to intermediate-type spirals. The decrease of CaT and CaT* with sigma contrasts with the well-known increase of another alpha-element index, Mg_2, with sigma. We discuss the role of Ca underabundance ([Ca/Fe]<0) and IMF variations in the onset of the observed relations.