  We report hints for the correlation between the X-ray and gamma-ray emission
in the nearby galaxy NGC 4945, which harbors both an active galactic nucleus
and a nuclear starburst region. We have divided the Fermi/LAT observations of
NGC 4945 into two datasets, comprising events detected during the low (L) and
high (H) level of X-ray emission from the active nucleus of this galaxy,
determined using the Swift/BAT light curve. Both datasets contain an equal
amount of 3.8 years of LAT data and NGC 4945 is detected with a similar
statistical significance of ~15 $\sigma$ in L and 14 $\sigma$ in H. However,
the slope of the gamma-ray spectrum hardens with the increase of the X-ray
flux, with the photon index $\Gamma$ = 2.47 +/- 0.07 in L and 2.11 +/- 0.08 in
H. The change is confirmed by a systematic variation of the spectral energy
distribution as well as a substantial reversal of the gamma-ray signal in
significance maps for low and high gamma-ray energies. The X/gamma-ray
correlation indicates that the gamma-ray production is dominated by the active
nucleus rather than by cosmic rays interacting with the interstellar medium. We
discuss possible locations of the gamma-ray source. We also compare NGC 4945
with other starburst galaxies detected by LAT and we note similarities between
those with active nuclei, e.g. unlikely high efficiencies of gamma-ray
production in starburst scenario, which argues for a significant contribution
of their active nuclei to the gamma-ray emission.
