We propose an experimental test of a scenario in the Next-to-Minimal Supersymmetric Standard Model in which both the lightest scalar and the lightest pseudoscalar Higgs bosons have masses around 125 GeV. The pseudoscalar can contribute significantly to the γγ rate at the LHC due to light Higgsino-like charginos in its effective one-loop coupling to two photons. Such charginos are obtained for small values of the µ eff parameter which also results in enhanced bb and τ + τ − rates compared to those expected for a Standard Model Higgs boson. This scenario should result in a clear discrepancy between the observed rates in these three decay channels and those in the W W and ZZ channels, since the pseudoscalar does not couple to the W and Z bosons. However, in the dominant gluon fusion production mode the pseudoscalar will stay hidden behind the SM-like scalar Higgs boson and in order for it to be observable the associated bbh production mode has to be considered, the cross section for which is tiny in the Standard Model but tan β-enhanced in supersymmetry. We analyze the constrained NMSSM with nonuniversal Higgs sector parameters and identify regions of its parameter space where the lightest pseudoscalar with mass around 125 GeV and strongly enhanced γγ (up to 60%), bb and τ + τ − rates in the bbh mode can be obtained. * On leave of absence from the University of Sheffield, UK.1 by the CMS have now fallen down to SM-like values, 0.78 ± 0.27 and 0.91 +0.30 −0.24 in the γγ and ZZ decay channels, respectively, with the mean value of the boson mass being 125.6 ± 0.64 GeV.The ATLAS collaboration, on the other hand, still reports sizable excesses, σ/σ SM = 1.65± 0.35 in the γγ channel with the mass measurement yielding 126.8 ± 0.73 GeV, and σ/σ SM = 1.7 ± 0.5 in the ZZ channel with mass at 124.3 +0.55 −0.4 GeV. Moreover, broad peaks consistent with a 125 GeV boson have now also been observed in the H → W W → 2l2ν channel in the two detectors. Importantly, the best-fit signal strength in this channel is SM-like according to both CMS and ATLAS, with a measured value of 0.76 ± 0.21 at the former and of 1.01 ± 0.31 at the latter. In the bb decay channel, although no significant excess has been observed above the SM background at either CMS or ATLAS, fitted signal strength values at m h = 125 GeV have been obtained by the two collaborations for some individual Higgs boson production modes. The best-fit values provided by the CMS collaboration read 0.7 ± 1.4 for vector boson fusion (VBF), 1.0 +0.5 −0.5 for Higgs-strahlung off a vector boson (W h/Zh) and 0.74 +1.34 −1.30 for associated production off top quarks (tth). The ATLAS collaboration has recently provided a fitted value of 0.2 ± 0.64 for the W h/Zh production mode only. In the τ + τ − channel an excess of events over a broad m h range was reported by the CMS collaboration with a best-fit σ/σ SM = 1.1 ± 0.4 at 125 GeV. At ATLAS, however, no excess has so far been observed in this channel also and a fitted value at m h = 125 GeV, which is SM-like but with a very large error,...