Natural Response of Parallel RLC Circuit
Let's write down equations in laplace form :

Z total = R || LS || 1/CS

Z total = R / [1+R(CS+1/LS)]

It is total impedance of circuit. If we assume initial conditions Vc0- = V0, and IL0- = I0, then for Ic we can write this equation:

Ic = Vc / Zc 

Ic = [I0 * Ztotal + V0] / (1/CS)

Ic = I0 * R / [ 1/CS + R(1+1/LCS^2)] + V0 * CS

This is current equation of Capacitor in laplace form.