We present HST STIS observations of the galaxy NGC 4382 (M85) and axisymmetric models of the galaxy to determine mass-to-light ration (M/L, V-band) and central black hole mass (M_BH). We find M/L = 3.74 +/- 0.1 (solar units) and M_BH = 1.3 (+5.2, -1.2) times 10^7 M_sun at an assumed distance of 17.9 Mpc, consistent with no black hole. The upper limit, M_BH < 9.6 times 10^7 M_sun (2{sigma}) or M_BH < 1.4 times 10^8 M_sun (3{sigma}) is consistent with the current M-{sigma} relation, which predicts M_BH = 8.8 times 10^7 M_sun at {sigma}_e = 182 km/s, but low for the current M-L relation, which predicts M_BH = 7.8 times 10^8 M_sun at L_V = 8.9 times 10^10 L_sun,V. HST images show the nucleus to be double, suggesting the presence of a nuclear eccentric stellar disk, in analogy to the Tremaine disk in M31. This conclusion is supported by the HST velocity dispersion profile. Despite the presence of this non-axisymmetric feature and evidence of a recent merger, we conclude that the reliability of our black hole mass determination is not hindered. The inferred low black hole mass may explain the lack of nuclear activity.