We present measurements of the near-infrared Ca II triplet (CaT, CaT*), Paschen (PaT), and magnesium (Mg I) 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 σ with small scatter. This dependence is similar to that recently found by Cenarro for elliptical galaxies, implying a uniform CaT*-σ relation that applies to galaxies from ellipticals to intermediate-type spirals. The decrease of CaT and CaT* with σ contrasts with the well-known increase of another α-element index, Mg2, with σ. We discuss the role of Ca underabundance ([Ca/Fe]<0) and initial mass function variations in the onset of the observed relations.