Muon spin rotation (μSR) experiments were performed on the intercalated graphite CaC6 in the normal and superconducting state down to 20 mK. In addition, AC magnetization measurements were carried out resulting in an anisotropic upper critical field , from which the coherence lengths ξ ab (0)=36.3(1.5) nm and ξ c (0)=4.3(7) nm were estimated. The anisotropy parameter TeX increases monotonically with decreasing temperature. A single isotropic s-wave description of superconductivity cannot account for this behavior. From magnetic field dependent μSR experiments, the absolute value of the in-plane magnetic penetration depth λ ab (0)=78(3) nm was determined. The temperature dependence of the superfluid density ρ s (T) is slightly better described by a two-gap than a single-gap model.