The classification of conformal Killing vector fields for FLRW space-time from Riemannian point of view was done by Maartens-Maharaj in \cite{Maartens1986}. In this paper, we introduce conformal Killing vector fields from statistical point of view and classify them for FLRW space-time. We also, obtain the conditions for vanishing the Lie derivative of affine connections with respect to conformal Killing vector fields. Finally, we study the Lie derivative of torsion tensor with respect to conformal Killing vector fields.