Multipole relaxation and transfer rates of the ${\rm 4s}^2$S, $3{\rm d}^2$D and $4{\rm p}^2$P states of Ca ii due to isotropic collisions with neutral hydrogen atoms are calculated. Evaluation of these rates have been carried out using accurate ab initio potential energy curves. The collisional T-matrix elements required for these calculations have been evaluated in a quantum mechanical description including fine structure splitting. Analytical expressions of all the rates valid for $200~{\rm K}\le T\le 10\,000$ K are given.