The (0,0)  2Π– 2Σ+ band of a cold molecular beam sample of magnesium monodeuteride, MgD, has been recorded field-free and in the presence of a static electric field of up to 11 kV/cm. The lines associated with the lowest rotational levels are detected for the first time. The field-free spectrum was analyzed to produce an improved set of fine structure parameters for the 2Π ( = 0) state. The observed electric field induced splittings and shifts were analyzed to produce permanent electric dipole moments, μ⃗ el of 2.567(10)D and 1.31(8)D for  2Π ( = 0) and  2Σ+( = 0) states, respectively. The recommended value for μ⃗ el ( 2Σ+ ( = 0)) for MgH, based upon the measured value for MgD, is 1.32(8)D.