  I cross-correlate the galaxy counts from the Canada-France Hawaii Telescope
Lensing Survey (CFHTLenS) galaxy catalogue and Cosmic Microwave Background
(CMB) convergence from the Planck data release 1 (2013) and 2 (2015), following
the work of Omori & Holder (2015). I improve their study by computing an
analytic covariance from the Halo Model, implementing simulations to validate
the theoretically estimated error bars and the reconstruction method, fitting
both a galaxy bias and a cross-correlation amplitude using the joint cross and
galaxy auto-correlation, and performing a series of null tests. Using a
bayesian analysis, I find a galaxy bias $b=0.92_{-0.02}^{+0.02}$ and a
cross-correlation amplitude $A=0.85_{-0.16}^{+0.15}$ for the 2015 release,
whereas for the 2013 release I find $b=0.93_{-0.02}^{+0.02}$ and
$A=1.05_{-0.15}^{+0.15}$. I thus confirm the difference between the two
releases found by Omori & Holder (2015), although both values of the amplitude
now appear to be compatible with the fiducial value $A=1$.
