  C-cyanomethanimine (HNCHCN), existing in the two $Z$ and $E$ isomeric forms,
is a key prebiotic molecule, but, so far, only the $E$ isomer has been detected
toward the massive star-forming region. Sagittarius B2(N) using transitions in
the radio wavelength domain. With the aim of detecting HNCHCN in Sun-like-star
forming regions, the laboratory investigation of its rotational spectrum has
been extended to the millimeter-/submillimeter-wave (mm-/submm-) spectral
window in which several unbiased spectral surveys have been already carried
out. High-resolution laboratory measurements of the rotational spectrum of
C-cyanomethanimine were carried out in the 100-420 GHz range using a
frequency-modulation absorption spectrometer. We then searched for the
C-cyanomethanimine spectral features in the mm-wave range using the
high-sensitivity and unbiased spectral surveys obtained with the IRAM 30-m
antenna in the ASAI context, the earliest stages of star formation from
starless to evolved Class I objects being sampled. For both the $Z$ and $E$
isomers, the spectroscopic work has led to an improved and extended knowledge
of the spectroscopic parameters, thus providing accurate predictions of the
rotational signatures up to $\sim$700 GHz. So far, no C-cyanomethanimine
emission has been detected toward the ASAI targets, and upper limits of the
column density of $\sim$ 10$^{11}$--10$^{12}$ cm$^{-2}$ could only be derived.
Consequently, the C-cyanomethanimine abundances have to be less than a few
10$^{-10}$ for starless and hot-corinos. A less stringent constraint, $\leq$
10$^{-9}$, is obtained for shocks sites. The combination of the upper limits of
the abundances of C-cyanomethanimine together with accurate laboratory
frequencies up to $\sim$ 700 GHz poses the basis for future higher sensitivity
searches around Sun-like-star forming regions.
