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.
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