  We present the results of simultaneous Suzaku and NuSTAR observations of the
nearest Low-Luminosity Active Galactic Nucleus (LLAGN), M81*. The spectrum is
well described by a cut-off power law plus narrow emission lines from Fe
K$\alpha$, Fe XXV and Fe XXVI. There is no evidence of Compton reflection from
an optically thick disc, and we obtain the strongest constraint on the
reflection fraction in M81* to date, with a best-fit value of $R = 0.0$ with an
upper limit of $R < 0.1$. The Fe K$\alpha$ line may be produced in optically
thin, $N_H = 1 \times 10^{23}$ cm$^{-2}$, gas located in the equatorial plane
that could be the broad line region. The ionized iron lines may originate in
the hot, inner accretion flow. The X-ray continuum shows significant
variability on $\sim 40$ ks timescales suggesting that the primary X-ray source
is $\sim 100$s of gravitational radii in size. If this X-ray source illuminates
any putative optically thick disc, the weakness of reflection implies that such
a disc lies outside a few $\times 10^3$ gravitational radii. An optically thin
accretion flow inside a truncated optically thick disc appears to be a common
feature of LLAGN that are accreting at only a tiny fraction of the Eddington
limit.
