Can the 126 GeV boson be a pseudoscalar?

We test the possibility that the newly discovered 126 GeV boson is a pseudoscalar by examining the correlations among the loop-induced pseudoscalar decay branching fractions to gamma gamma, ZZ*, Z gamma, and WW* final states in a model-independent way. These four decays are controlled by only two effective operators, so that the rates in Z gamma and WW* are predicted now that the rates in gamma gamma and ZZ*, Z gamma* -> 4l have been measured. We find that the pseudoscalar possibility is disfavored but not conclusively excluded. Experimental exclusion of the Z gamma decay to well below sigma/sigma(SM) similar to 170 or conclusive observation of the WW* decay near the Standard Model rate would eliminate the pseudoscalar possibility. The Z gamma exclusion should be possible using existing data. The only loophole in our argument is the possibility that the 4l signal comes from pseudoscalar decays to a pair of new neutral gauge bosons with mass near the Z pole.