Alpha particles following the beta decay of B12 and the positron decay of N12 to the region of C12 above the 7.66-MeV state have been observed using a solid-state counter. The two alpha-particle spectra differ considerably in form and intensity but are completely consistent with one another within the assumption of charge symmetry. Since transitions to a possible admixed T=1 component in C12 would be coherent with those to the chief T=0 component and since the matrix elements to these two components add in one decay and subtract in the other, the test of charge symmetry is quite sharp and it is shown that the intensity of the T=1 impurity may well be less than 1%. The branching ratios for the production of these high-energy alpha particles are (7+/-2)×10-4 and (4.4+/-1.5)×10-3 in the decay of B12 and N12, respectively. A reasonable account of the alpha-particle spectrum following N12 decay (and so, by implication, following B12 decay) is given by a single very broad J=0+ level at a nominal resonance energy of 5.0 MeV above Be8+α and a reduced width of 2.6 single-particle units (3ℏ22MR2). A better account is given by a broad level at lower excitation plus a level at about 11.8 MeV to which the N12 beta decay has ft~4.6. The possible origin of the alpha-particle spectra in terms of the "ghost" of the 7.66-MeV state is considered and it is concluded that while such an effect may be quite considerable it is unlikely to account for the whole spectra as observed in this work.