  We theoretically investigate the subgapped transport phenomena through a
normal-superconductor-normal (NSN) junction made up of ultra thin topological
insulator with proximity induced superconductivity. The dimensional crossover
from three dimensional ($3$D) topological insulator (TI) to thin
two-dimensional ($2$D) TI introduces a new degree of freedom, the so-called
hybridization or coupling between the two surface states. We explore the role
of hybridization in transport properties of the NSN junction, especially how it
affects the crossed Andreev reflection (CAR). We observe that a rib-like
pattern appears in CAR probability profile while examined as a function of
angle of incidence and length of the superconductor. Depending on the incoming
and reflection or transmission channel, CAR probability can be maneuvered to be
higher than $97\%$ under suitable coupling between the two TI surface states
along with appropriate gate voltage and doping concentration in the normal
region. Coupling between the two surfaces also induces an additional
oscillation envelope in the behavior of the angle averaged conductance, with
the variation of the length of the superconductor. The behavior of co-tunneling
(CT) probability is also very sensitive to the coupling and other parameters.
Finally, we also explore the shot noise cross correlation and show that the
behavior of the same can be monotonic or non-monotonic depending on the doping
concentration in the normal region. Under suitable circumstances, shot noise
cross correlation can change sign from positive to negative or vice versa
depending on the relative strength of CT and CAR.
