We investigate the dependence of the center-of-mass tomogram of a system with many degrees of freedom N on Planck's constant . It is shown that the use of the central limit theorem at N→+∞ in the quantum case can be employed for checking the condition of its validity in the famous Lyapunov form. In this case, the resulting distribution is Gaussian if the initial distribution is a product of either independent excited states of a quantum oscillator or even and odd coherent states. Then, at Planck's constant → 0, one gets the δ-function associated with the distribution with the maximum at zero and with the probability equal to one.