  We present the results of a study of the amount and distribution of cold
atomic gas, as well its correlation with recent star formation in a sample of
extremely faint dwarf irregular galaxies. Our sample is drawn from the Faint
Irregular Galaxy GMRT Survey (FIGGS) and its extension, FIGGS2. We use two
different methods to identify cold atomic gas. In the first method,
line-of-sight HI spectra were decomposed into multiple Gaussian components and
narrow Gaussian components were identified as cold HI. In the second method,
the brightness temperature (T_B) is used as a tracer of cold HI. We find that
the amount of cold gas identified using the T_B method is significantly larger
than the amount of gas identified using Gaussian decomposition. We also find
that a large fraction of the cold gas identified using the T_B method is
spatially coincident with regions of recent star formation, although the
converse is not true. That is only a small fraction of the regions with recent
star formation are also covered by cold gas. For regions where the star
formation and the cold gas overlap, we study the relationship between the star
formation rate density and the cold \HI column density. We find that the star
formation rate density has a power law dependence on the HI column density, but
that the slope of this power law is significantly flatter than that of the
canonical Kennicutt-Schmidt relation.
