  Efforts are underway to set up an underground laboratory in India for rare
event studies like double beta decay, dark matter, etc. For such experiments,
mitigation of radiation background is of paramount importance and understanding
ambient background at the site, originating from the rock, is one of the
crucial factors. With this motivation, the radiopurity studies of a rock sample
from the potential laboratory site in the Aut tunnel of Himachal Pradesh
(India) have been carried out using the TIFR low background experimental setup
(TiLES). The concentration of $^{40}$K in Aut rock is observed to be lower by a
factor of ~1000 as compared to the samples from BWH (Bodi West Hill), Tamil
Nadu (India), current designated site for India-based Neutrino Observatory. The
natural radioactive trace impurity $^{232}$Th is lower in the Aut rock, while
$^{238}$U is somewhat higher than the BWH rock. Overall, the ambient gamma ray
background at Aut is expected to be lower than the BWH, while ambient neutron
background is expected to be similar. Further, to assess the neutron-induced
long lived activity, fast neutron activation studies have been carried out on
the both Aut and BWH rock samples at the Pelletron Linac Facility, Mumbai.
