  We have studied HI absorption towards three non-thermal filaments (NTFs)
Sgr-C, G359.54+0.18 and G359.79+0.17 using the Giant Metrewave Radio Telescope
(GMRT). Our study, for the first time, constrains the distance of the Sgr C NTF
and the HII region seen associated with the NTF in the sky plane, to within a
few hundred parsecs from the Galactic Centre (GC). A molecular cloud with a
velocity of -100 km/s appears to be associated with the central part of the Sgr
C NTF. Our study also indicates that the Sgr C HII region is relatively farther
away than the NTF along our line of sight, and thereby provides evidence
against any possible interaction between the two objects. The NTF G359.54+0.18
shows weak HI absorption (4 sigma detection) at a velocity of -140 km/s, which
is the velocity of a known dense molecular cloud seen towards the NTF. This
cloud is expected to be located within ~200 pc from the GC and thereby provides
a lower limit to the distance. The upper limit to the distance of this NTF from
the Sun is 10.5 kpc. The distance to the NTF G359.79+0.17 is between 5.1 and
10.5 kpc from the Sun.
