We present a detailed analysis of the dayside atmosphere of the hot-Neptune GJ 436b, based on recent Spitzer observations. We report statistical constraints on the thermal and chemical properties of the planetary atmosphere, study correlations between the various molecular species, and discuss scenarios of equilibrium and non-equilibrium chemistry in GJ 436b. We model the atmosphere with a one-dimensional line-by-line radiative transfer code with parameterized molecular abundances and temperature structure. We explore the model parameter space with 10 6 models, using a Markov chain Monte Carlo scheme. Our results encompass previous findings, indicating a paucity of methane, an overabundance of CO and CO 2 , and a slight underabundance of H 2 O, as compared to equilibrium chemistry with solar metallicity. The concentrations of the species are highly correlated. Our best-fit, and most plausible, constraints require a CH 4 mixing ratio of 10 −7 to 10 −6 , with CO 10 −3 , CO 2 ∼ 10 −6 to 10 −4 , and H 2 O 10 −4 ; higher CH 4 would require much higher CO and CO 2 . Based on calculations of equilibrium and non-equilibrium chemistry, we find that the observed abundances can potentially be explained by a combination of high metallicity (∼10× solar) and vertical mixing with K zz ∼ 10 6 -10 7 cm 2 s −1 . The inferred metallicity is enhanced over that of the host star which is known to be consistent with solar metallicity. Our constraints rule out a dayside thermal inversion in GJ 436b. We emphasize that the constraints reported in this work depend crucially on the observations in the two Spitzer channels at 3.6 μm and 4.5 μm. Future observations with warm Spitzer and with the James Webb Space Telescope will be extremely important to improve upon the present constraints on the abundances of carbon species in the dayside atmosphere of GJ 436b.