Analyses are reported on properties of the recently discovered Higgs-like resonance around 125~GeV in its decay to two photons. The analyses are performed using the 2011 (2012) dataset recorded by the CMS experiment at the LHC from $pp$ collisions at a centre-of-mass energy of 7 (8)~TeV. The dataset corresponds to an integrated luminosity of 5.1 (19.6)~fb$^{-1}$. The spin analysis is evaluated on the 2012 dataset alone. An upper limit on the natural width of the observed resonance is found to be 6.9~GeV at 95\% confidence level. A search has been performed for second Higgs-like states in the range 110 $<m_{H}<$ 150~GeV. Spin hypothesis tests have been performed comparing the Standard Model Higgs with a spin-2 graviton-like model with minimal couplings. The current data cannot exclude this particular model of spin-2 whilst the data are compatible with the Standard Model Higgs at the 1$\sigma$ level.

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