  The chirality suggested for the doublet bands B2 and B2a in $^{195}$Tl in
$A\sim190$ region is reexamined. The potential-energy curves and the
configurations together with the deformation parameters are obtained by the
constrained covariant density functional theory. The corresponding experimental
energy spectra, energy differences between doublet bands, and the available
$B(M1)/B(E2)$ values are investigated by the fully quantal particle rotor
model. Analysis on the basis of the angular momentum components, the $K$-plots,
and the azimuthal plots suggest a planar rotation interpretation for the bands
B2 and B2a. Hence, it coexists with the aplanar rotation in the other doublet
bands B4 and B4a in $^{195}$Tl.
