  CaSb$_2$ is a bulk superconductor and a topological semimetal, making it a
great platform for realizing topological superconductivity. In this work, we
investigate the superconducting upper and lower critical field anisotropy using
magnetic susceptibility, and study the superconducting state using muon
spin-relaxation. The temperature dependence of transverse-field relaxation rate
can be fitted with a single-gap model or two-gap model. Zero-field relaxation
shows little temperature dependence when the muon-spin is parallel to the
$c*$-axis, while an increase in relaxation appears below 1 K when the muon-spin
is parallel to the $ab$-plane. We conclude an $s+is$ order parameter
considering the breaking of time-reversal symmetry (TRS), which originates from
competing interband interactions between the three bands of CaSb$_2$. To
explain the direction-dependent breaking of TRS we suggest loop currents
developing in the plane of distorted square-net of Sb atoms.
