  In this paper we present an analytic framework for formulating the
statistical distribution of the nearest neighbour distance in hard-core point
processes. We apply this framework to Mat\'{e}rn hard-core point process (MHC)
to derive the cumulative distribution function of the contact distance in three
cases. The first case is between a point in an MHC process and its nearest
neighbour from the same process. The second case is between a point in an
independent Poisson point process and the nearest neighbour from an MHC
process. The third case is between a point in the complement of an MHC process
and its sibling MHC process. We test the analytic results against Monte-Carlo
simulations to verify their consistency.
