  Several recent works have reported the detection of an unidentified X-ray
line at 3.55~keV, which could possibly be attributed to the decay of dark
matter (DM) particles in the halos of galaxy clusters and in the M31 galaxy. We
analyze all publicly-available XMM-Newton data of dwarf spheroidal galaxies to
test the possible DM origin of the line. Dwarf spheroidal galaxies have high
mass-to-light ratios and their interstellar medium is not a source of diffuse
X-ray emission, thus they are expected to provide the cleanest DM decay line
signal. Our analysis shows no evidence for the presence of the line in the
stacked spectra of the dwarf galaxies. It excludes the sterile neutrino DM
decay origin of the 3.5 keV line reported by Bulbul et al. (2014) at the level
of 4.1sigma under standard assumptions about the Galactic DM column density in
the direction of selected dwarf galaxies and at the level of 3.2sigma assuming
minimal Galactic DM column density. Our analysis is still consistent with the
estimate of sterile neutrino DM parameters by Boyarsky et al. (2014), because
of its larger uncertainty. However, the central value of their estimate of the
mixing angle is inconsistent with our dwarf spheroidals data at 3.4sigma
(2.5sigma) level assuming the mean (minimal) Galactic DM column density. As a
by-product of our analysis, we provide updated upper limits to the mixing angle
of sterile neutrino DM in the mass range between 2 and 20 keV.
