  Compounds with kagome lattice usually host many exotic quantum states,
including the quantum spin liquid, non-trivial topological Dirac bands and a
strongly renormalized flat band, etc. Recently an interesting vanadium based
kagome family $A$V$_{3}$Sb$_{5}$ ($A$ = K, Rb, or Cs) was discovered, and these
materials exhibit multiple interesting properties, including unconventional
saddle-point driving charge density wave (CDW) state, superconductivity, etc.
Furthermore, some experiments show anomalous Hall effect which inspires that
there might be some chiral flux current states. Here we report scanning
tunneling measurements by using spin-polarized tips. Although we have observed
clearly the $2a_0\times2a_0$ CDW and $4a_0$ stripe orders, the well-designed
experiments with refined spin-polarized tips do not reveal any trace of the
chiral flux current phase in CsV$_3$Sb$_5$ within the limits of experimental
accuracy. No observation of the local magnetic moment in our experiments may
put an upper bound constraint on the magnitude of magnetic moments induced by
the possible chiral loop current which has a time-reversal symmetry breaking
along $c$-axis in CsV$_{3}$Sb$_{5}$.
