The γ rays following the decay of Se81m (T12=57 min) and Se81 (T12=18 min) were investigated using a Ge(Li) detector, a γ-γ coincidence apparatus, and a high-pressure gas proportional counter. Se81m and Se81 were produced by neutron bombardment of 94.4% enriched Se80 and natural selenium. Nine γ rays have been identified as belonging to the decay of Se81m and Se81 by using the Ge(Li) detector. The energies (in keV) and relative intensities (in brackets) of these γ rays are as follows. Se81m: 103.3+/-0.2 (100) and 1146+/-2 (3.4+/-0.6). Se81: 276.3+/-0.4 (100), 290.2+/-0.4 (79.6+/-5.6), 538.7+/-0.7 (6.2+/-0.7), 552.7+/-0.7 (12.8+/-1.4), 566.1+/-0.7 (28.9+/-2.6), 650.4+/-0.9 (2.6+/-0.4), and 829.2+/-0.8 (36.6+/-2.6). A γ ray of energy 180+/-2 keV (relative intensity=0.94+/-0.19) has also been attributed to Se81 through γ-γ coincidence measurements. An energy-level scheme of Br81 populated by the decay of Se81m and Se81 has been proposed by introducing levels at 276, 566, 650, 815, 829, and 1146 keV. The 1146-keV level is fed by a direct β decay of Se81m with a transition intensity of (0.34+/-0.13)%. The β-decay transition intensities of Se81 to the 0-, 566-, 650-, 815-, and 829-keV levels of Br81 were computed to be (98.8+/-0.33)%, (0.76+/-0.21)%, (0.014+/-0.006)%, (0.042+/-0.013)%, and (0.36+/-0.10)%, respectively.