The first and second excited states of 27 Si have been populated by the reaction 28 Si( 3 He, α) 27 Si. The particle-gamma-ray angular correlation associated with the decay of the first excited state is consistent with J = ½ for this state. The data on the second excited state are satisfied by J = 3/2, 7/2. The decay modes of these states are compared with those of the analogous states in 27 Al.