  The supernova SN 2005cz has recently attracted some attention, due to the
fact that it was spectroscopically similar to type Ib supernovae (SNe), a class
that is presumed to result from core-collapse of massive stars, yet it occurred
in an elliptical galaxy, where one expects very few massive stars to exist. Two
explanations for this remarkable event were put forward. Perets et al. (2010)
associate SN 2005cz with the class of Ca-rich, faint SNe Ib, which likely
result from old double-white-dwarf systems with a He-rich secondary. On the
other hand, Kawabata et al. (2010) suggest that SN 2005cz is indeed a
core-collapse event (in a binary system), albeit of a star at the lower end of
the mass range, 10-12 M_Sun. The existence of this star in its elliptical host
is explained as resulting from low-level star formation (SF) activity in that
galaxy. Here we present extensive observations of the location of SN 2005cz,
sensitive to a variety of SF tracers, including optical spectroscopy, H_alpha
emission, UV emission and HST photometry. We show that NGC 4589, the host
galaxy of SN 2005cz, does not show any signatures of a young stellar population
or recent SF activity either close to or far from the location of SN 2005cz.
